Package 'UComp'

Title: Automatic Univariate Time Series Modelling of many Kinds
Description: Comprehensive analysis and forecasting of univariate time series using automatic time series models of many kinds. Harvey AC (1989) <doi:10.1017/CBO9781107049994>. Pedregal DJ and Young PC (2002) <doi:10.1002/9780470996430>. Durbin J and Koopman SJ (2012) <doi:10.1093/acprof:oso/9780199641178.001.0001>. Hyndman RJ, Koehler AB, Ord JK, and Snyder RD (2008) <doi:10.1007/978-3-540-71918-2>. Gómez V, Maravall A (2000) <doi:10.1002/9781118032978>. Pedregal DJ, Trapero JR and Holgado E (2024) <doi:10.1016/j.ijforecast.2023.09.004>.
Authors: Diego J. Pedregal [aut, cre] (ORCID: <https://orcid.org/0000-0003-4958-0969>)
Maintainer: Diego J. Pedregal <[email protected]>
License: GPL-3
Version: 5.3.1
Built: 2026-06-03 07:13:25 UTC
Source: https://github.com/cran/UComp

Help Index

Accuracy

Description

Accuracy for 1 time series y and several forecasting methods py and h steps ahead py is h x nMethods x nSeries

Usage

Accuracy(py, y, s = frequency(y), collectFun = mean)

Arguments

py

matrix of forecasts (h x nMethods x nForecasts)
y

a matrix of actual values (n x nForecasts)
s

seasonal period, number of observations per year
collectFun

aggregation function (mean, median, etc.)

Value

Table of accuracy results

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, tsDisplay, size

Examples

## Not run: Accuracy(py, y, 12)

acft

Description

Theoretical autocorrelation functions of ARMA models

Usage

acft(MApoly = 1, ARpoly = 1, ncoef = 38, s = 1)

Arguments

MApoly

coefficients of numerator polynomial in descending order
ARpoly

coefficients of denominator polynomial in descending order
ncoef

number of coefficients
s

seasonal period, number of observations per year

Value

Theoretical autocorrelation functions

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, slide, plotSlide, Accuracy, tsDisplay, size

Examples

acft(c(1, -0.8), c(1, 0.8))

AIC.UComp

Description

Extract AIC value of UComp object

Usage

## S3 method for class 'UComp'
AIC(object, ..., k = 2)

Arguments

object

Object of class “UComp”.
...

Additional inputs to function.
k

The penalty per parameter to be used.

Details

Selection criteria for models with different number of parameters, the smaller AIC the better. The formula used here is AIC=−2(ln(L)−k)/nAIC=-2 (ln(L) - k) / n, where ln(L)ln(L) is the log-likelihood at the optimum, kk is the number of parameters plus non-stationary states and nn is the number of observations. Mind that this formulation differs from the usual definition that does not divide by nn. This makes that AIC(m) and AIC(logLik(m)) give different results, being m an UComp object.

Value

AIC value of a UC model

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents

Examples

y <- log(AirPassengers)
m1 <- UCforecast(y, model = "llt/equal/arma(0,0)")
AIC(m1)

Airpassengers in Spain

Description

Foreign arrivals by air in Spain in thousands of passengers (airpas).

Usage

airpas

Format

Time series objects.

Monthly data from 1969

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Value

No return value, called for side effects

Examples

airpas

ARIMA

Description

Runs all relevant functions for ARIMA modelling

Usage

ARIMA(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. A vector c(p,d,q,P,D,Q) containing the model orders of an ARIMA(p,d,q)x(P,D,Q)_s model. A constant may be estimated with the cnst input. Use a NULL to automatically identify the ARIMA model.
cnst

flag to include a constant in the model (TRUE/FALSE/NULL). Use NULL to estimate
s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
criterion

information criterion for identification stage ("aic", "bic", "aicc")
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
verbose

intermediate estimation output (TRUE / FALSE)
lambda

Box-Cox lambda parameter (NULL: estimate)
maxOrders

a vector c(p,d,q,P,D,Q) containing the maximum orders of model orders to search for in the automatic identification
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
fast

fast identification (avoids post-identification checks)

Details

See help of ARIMAforecast.

Value

An object of class ARIMA. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any ARIMA object as specified in what follows (function ARIMA fills in all of them at once):

After running ARIMAforecast or ARIMA:

p

Estimated parameters
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running ARIMAvalidate:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

See Also

ARIMAforecast, ARIMAvalidate,

Examples

y <- log(AirPassengers)
m1 <- ARIMA(y)
m1 <- ARIMA(y, lambda = NULL)

ARIMAestim

Description

Estimates and forecasts ARIMA models

Usage

ARIMAestim(m)

Arguments

m

an object of type ARIMA created with ARIMAforecast

Details

ARIMAestim estimates and forecasts a time series using an ARIMA model

Value

The same input object with the appropriate fields filled in, in particular:

p

Estimated parameters
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

ARIMAforecast

Description

Estimates and forecasts ARIMA general univariate models

Usage

ARIMAforecast(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. A vector c(p,d,q,P,D,Q) containing the model orders of an ARIMA(p,d,q)x(P,D,Q)_s model. A constant may be estimated with the cnst input. Use a NULL to automatically identify the ARIMA model.
cnst

flag to include a constant in the model (TRUE/FALSE/NULL). Use NULL to estimate
s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
criterion

information criterion for identification stage ("aic", "bic", "aicc")
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
verbose

intermediate estimation output (TRUE / FALSE)
lambda

Box-Cox lambda parameter (NULL: estimate)
maxOrders

a vector c(p,d,q,P,D,Q) containing the maximum orders of model orders to search for in the automatic identification
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
fast

fast identification (avoids post-identification checks)

Details

ARIMAforecast is a function for modelling and forecasting univariate time series with Autoregressive Integrated Moving Average (ARIMA) time series models. It sets up the model with a number of control variables that govern the way the rest of functions in the package will work. It also estimates the model parameters by Maximum Likelihood and forecasts the data.

Value

An object of class ARIMA. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any ARIMA object as specified in what follows (function ARIMA fills in all of them at once):

After running ARIMAforecast or ARIMA:

p

Estimated parameters
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running ARIMAvalidate:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

See Also

ARIMA, ARIMAvalidate,

Examples

y <- log(AirPassengers)
m1 <- ARIMAforecast(y)
m1 <- ARIMAforecast(y, lambda = NULL)

ARIMAsetup

Description

Sets up ARIMA general models

Usage

ARIMAsetup(
  y,
  u = NULL,
  model = NULL,
  cnst = NULL,
  s = frequency(y),
  criterion = "bic",
  h = 2 * s,
  verbose = FALSE,
  lambda = 1,
  maxOrders = c(3, 2, 3, 2, 1, 2),
  bootstrap = FALSE,
  nSimul = 5000,
  fast = FALSE
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. A vector c(p,d,q,P,D,Q) containing the model orders of an ARIMA(p,d,q)x(P,D,Q)_s model. A constant may be estimated with the cnst input. Use a NULL to automatically identify the ARIMA model.
cnst

flag to include a constant in the model (TRUE/FALSE/NULL). Use NULL to estimate
s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
criterion

information criterion for identification stage ("aic", "bic", "aicc")
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
verbose

intermediate estimation output (TRUE / FALSE)
lambda

Box-Cox lambda parameter (NULL: estimate)
maxOrders

a vector c(p,d,q,P,D,Q) containing the maximum orders of model orders to search for in the automatic identification
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
fast

fast identification (avoids post-identification checks)

Details

See help of ARIMAforecast.

Value

An object of class ARIMA. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any ARIMA object as specified in what follows (function ARIMA fills in all of them at once):

After running ARIMAforecast or ARIMA:

p

Estimated parameters
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running ARIMAvalidate:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

See Also

ARIMA, ARIMAforecast, ARIMAvalidate,

Examples

y <- log(AirPassengers)
m1 <- ARIMAsetup(y)
m1 <- ARIMAsetup(y, lambda = NULL)

ARIMAvalidate

Description

Shows a table of estimation and diagnostics results for ARIMA models

Usage

ARIMAvalidate(m)

Arguments

m

an object of type ARIMA created with ARIMAforecast

Value

The same input object with the appropriate fields filled in, in particular:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

See Also

ARIMA, ARIMAforecast, ARIMAvalidate,

Examples

m1 <- ARIMAforecast(log(gdp))
m1 <- ARIMAvalidate(m1)

arma2tsi

Description

AR polynomial coefficients of ARMA model

Usage

arma2tsi(MApoly, ARpoly, n = 100)

Arguments

MApoly

coefficients of numerator polynomial in descending order
ARpoly

coefficients of denominator polynomial in descending order
n

number of coefficients

Value

Tsi (MA form) coefficients of equivalent ARMA model

Author(s)

Diego J. Pedregal

armaFilter

Description

Filter of time series

Usage

armaFilter(MA = 1, AR = 1, y)

Arguments

MA

numerator polynomial
AR

denominator polynomial
y

a vector, ts or tsibble object

Value

Filtered time series

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

y <- armaFilter(1, c(1 , -0.8), rnorm(200))

auxInvBoxCox

Description

Inverse of Box-Cox transformation

Usage

auxInvBoxCox(y, lambda)

Arguments

y

matrix, array or vector
lambda

lambda parameter of Box-Cox transformation

Value

Inverse of Box-Cox heteroskedasticity transformation

Author(s)

Diego J. Pedregal

BIC.UComp

Description

Extract BIC (or SBC) value of UComp object

Usage

## S3 method for class 'UComp'
BIC(object, ...)

Arguments

object

Object of class “UComp”.
...

Additional inputs to function.

Details

Selection criteria for models with different number of parameters, the smaller BIC the better. The formula used here is BIC=(−2ln(L)+kln(n))/nBIC=(-2 ln(L) + k ln(n)) / n, where ln(L)ln(L) is the log-likelihood at the optimum, kk is the number of parameters plus non-stationary states and nn is the number of observations. Mind that this formulation differs from the usual definition that does not divide by nn. This makes that BIC(m) and BIC(logLik(m)) give different results, being m an UComp object.

Value

BIC value of a UC model

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents

Examples

y <- log(AirPassengers)
m1 <- UCforecast(y, model = "llt/equal/arma(0,0)")
BIC(m1)

box.cox

Description

Runs Box-Cox transform of a time series

Usage

box.cox(x, lambda)

Arguments

x

Time series object.
lambda

Lambda parameter for Box-Cox transform.

Value

Box-Cox transformed time series

Author(s)

Diego J. Pedregal

See Also

inv.box.cox, UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents

Examples

y <- box.cox(AirPassengers, 0.5)
plot(y)

Methane concentration at Cape Grim in Australia

Description

Methane concentration at Cape Grim in Australia (ch4).

Usage

ch4

Format

Time series objects.

Monthly data from January 1992 to December 2019

Value

No return value, called for side effects

Source

CH4 data

Examples

ch4

colMedians

Description

Medians of matrix by columns

Usage

colMedians(x, na.rm = TRUE, ...)

Arguments

x

a matrix
na.rm

boolean indicating whether to remove nans
...

rest of inputs

Value

A vector with all the medians in columns

Author(s)

Diego J. Pedregal

See Also

rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

s <- colMedians(matrix(4, 3, 2))

conv

Description

1D convolution: filtering or polynomial multiplication

Usage

conv(...)

Arguments

...

list of vectors to convolute

Value

Convolution of all input vectors

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

conv(c(1, -1), c(1, -2, 1))
conv(c(1, -1), c(1, 0.8))

cusum

Description

Cusum and cusumsq tests

Usage

cusum(y, runFromTest = FALSE)

Arguments

y

a vector, ts or tsibble object
runFromTest

internal check variable

Value

No return value, called for side effects

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

cusum(AirPassengers)

DAYforecast

Description

Estimates and forecasts daily time series with weekly and monthly seasonal patterns

Usage

DAYforecast(
  y,
  u = NULL,
  initial_date,
  h = 24,
  lambda = 1,
  criterion = "aic",
  p0 = -9999.9,
  verbose = FALSE
)

Arguments

y

A numeric vector, ts object or list containing daily observations of the dependent variable.
u

Optional matrix or vector of exogenous regressors. If provided, it must cover both the estimation and forecast periods.
initial_date

A character or Date object indicating the calendar start date of the series.
h

Integer indicating the forecast horizon (number of days ahead).
lambda

Box–Cox transformation parameter (NULL for automatic identification).
criterion

Information criterion used for model selection (AIC, BIC, AICc).
p0

Initial parameter vector for Maximum Likelihood estimation.
verbose

if TRUE, prints estimation details.

Details

DAYforecast estimates and forecasts daily univariate time series using Dynamic Harmonic Regression (DHR).

The function is tailored for daily data and explicitly accounts for:

  • Monthly seasonality through sinusoidal terms based on calendar months

  • Weekly seasonality through sinusoidal terms with periods of 7 days

Standard methods applicable to UComp objects are available.

Value

An object of class UComp. It is a list containing the model specification, estimated parameters, and forecasting results.

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCfilter, UCsmooth, UCdisturb, UCcomponents

Examples

y <- rnorm(400)
m <- DAYforecast(y, initial_date = "2015-01-01", h = 30)

dif

Description

Discrete differencing of time series

Usage

dif(y, difs = 1, seas = 1)

Arguments

y

a vector, ts or tsibble object
difs

vector with differencing orders
seas

vector of seasonal periods

Value

Differenced time series

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

dif(AirPassengers)
dif(AirPassengers, 2)
dif(AirPassengers, c(1, 1), c(1, 12))

ETS

Description

Runs all relevant functions for ETS modelling

Usage

ETS(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component with one or two letters:

  • Error: ? / A / M

  • Trend: ? / N / A / Ad / M / Md

  • Seasonal: ? / N / A / M

s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
criterion

information criterion for identification ("aic", "bic" or "aicc").
lambda

Box-Cox lambda parameter (NULL: estimate)
armaIdent

check for arma models for error component (TRUE / FALSE).
identAll

run all models to identify the best one (TRUE / FALSE)
forIntervals

estimate forecasting intervals (TRUE / FALSE)
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
verbose

intermediate estimation output (TRUE / FALSE)
alphaL

constraints limits for alpha parameter
betaL

constraints limits for beta parameter
gammaL

constraints limits for gamma parameter
phiL

constraints limits for phi parameter
p0

initial values for parameter search (alpha, beta, phi, gamma) with consraints:

  • 0 < alpha < 1

  • 0 < beta < alpha

  • 0 < phi < 1

  • 0 < gamma < 1 - alpha

Details

See help of ETSforecast.

Value

An object of class ETS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any ETS object as specified in what follows (function ETS fills in all of them at once):

After running ETSforecast:

p

Estimated parameters
criteria

Values for estimation criteria (LogLik, AIC, BIC, AICc)
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running ETSvalidate:

table

Estimation and validation table
comp

Estimated components in matrix form

After running ETScomponents:

comp

Estimated components in matrix form

An object of class ETS. See ETSforecast.

Author(s)

Diego J. Pedregal

See Also

ETSforecast, ETSvalidate, ETScomponents

Examples

y <- log(AirPassengers)
m1 <- ETS(y)
m1 <- ETS(y, model = "MAM")

ETScomponents

Description

Estimates components of ETS models

Usage

ETScomponents(m)

Arguments

m

an object of type ETS created with ETSforecast

Value

The same input object with the appropriate fields filled in, in particular:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

See Also

ETS, ETSforecast, ETSvalidate

Examples

m1 <- ETS(log(gdp))
m1 <- ETScomponents(m1)

ETSestim

Description

Estimates and forecasts ETS models

Usage

ETSestim(m)

Arguments

m

an object of type ETS created with ETSforecast

Details

ETSestim estimates and forecasts a time series using an an ETS model

Value

The same input object with the appropriate fields filled in, in particular:

p

Estimated parameters
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

Author(s)

Diego J. Pedregal

See Also

ETS, ETSforecast, ETSvalidate, ETScomponents

Examples

m1 <- ETSsetup(log(gdp))
m1 <- ETSestim(m1)

ETSforecast

Description

Estimates and forecasts ETS general univariate models

Usage

ETSforecast(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = max(2 * s, 6),
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component with one or two letters:

  • Error: ? / A / M

  • Trend: ? / N / A / Ad / M / Md

  • Seasonal: ? / N / A / M

s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
criterion

information criterion for identification ("aic", "bic" or "aicc").
lambda

Box-Cox lambda parameter (NULL: estimate)
armaIdent

check for arma models for error component (TRUE / FALSE).
identAll

run all models to identify the best one (TRUE / FALSE)
forIntervals

estimate forecasting intervals (TRUE / FALSE)
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
verbose

intermediate estimation output (TRUE / FALSE)
alphaL

constraints limits for alpha parameter
betaL

constraints limits for beta parameter
gammaL

constraints limits for gamma parameter
phiL

constraints limits for phi parameter
p0

initial values for parameter search (alpha, beta, phi, gamma) with consraints:

  • 0 < alpha < 1

  • 0 < beta < alpha

  • 0 < phi < 1

  • 0 < gamma < 1 - alpha

Details

ETSforecast is a function for modelling and forecasting univariate time series with ExponenTial Smoothing (ETS) time series models. It sets up the model with a number of control variables that govern the way the rest of functions in the package will work. It also estimates the model parameters by Maximum Likelihood and forecasts the data.

Value

An object of class ETS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any ETS object as specified in what follows (function ETS fills in all of them at once):

After running ETSforecast:

p

Estimated parameters
criteria

Values for estimation criteria (LogLik, AIC, BIC, AICc)
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running ETSvalidate:

table

Estimation and validation table
comp

Estimated components in matrix form

After running ETScomponents:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

See Also

ETS, ETSvalidate, ETScomponents

Examples

y <- log(AirPassengers)
m1 <- ETSforecast(y)
m1 <- ETSforecast(y, model = "A?A")

ETSsetup

Description

Sets up ETS general univariate models

Usage

ETSsetup(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  lambda = 1,
  armaIdent = FALSE,
  identAll = FALSE,
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(1e-08, 1 - 1e-08),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component with one or two letters:

  • Error: ? / A / M

  • Trend: ? / N / A / Ad / M / Md

  • Seasonal: ? / N / A / M

s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
criterion

information criterion for identification ("aic", "bic" or "aicc").
lambda

Box-Cox lambda parameter (NULL: estimate)
armaIdent

check for arma models for error component (TRUE / FALSE).
identAll

run all models to identify the best one (TRUE / FALSE)
forIntervals

estimate forecasting intervals (TRUE / FALSE)
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
verbose

intermediate estimation output (TRUE / FALSE)
alphaL

constraints limits for alpha parameter
betaL

constraints limits for beta parameter
gammaL

constraints limits for gamma parameter
phiL

constraints limits for phi parameter
p0

initial values for parameter search (alpha, beta, phi, gamma) with consraints:

  • 0 < alpha < 1

  • 0 < beta < alpha

  • 0 < phi < 1

  • 0 < gamma < 1 - alpha

Details

See help of ETSforecast.

Value

An object of class ETS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any ETS object as specified in what follows (function ETS fills in all of them at once):

After running ETSforecast:

p

Estimated parameters
criteria

Values for estimation criteria (LogLik, AIC, BIC, AICc)
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running ETSvalidate:

table

Estimation and validation table
comp

Estimated components in matrix form

After running ETScomponents:

comp

Estimated components in matrix form

An object of class ETS. See ETSforecast.

Author(s)

Diego J. Pedregal

See Also

ETS, ETSforecast, ETSvalidate, ETScomponents

Examples

y <- log(AirPassengers)
m1 <- ETSsetup(y)
m1 <- ETSsetup(y,  model = "???")
m1 <- ETSsetup(y,  model = "?AA")

ETSvalidate

Description

Shows a table of estimation and diagnostics results for ETS models

Usage

ETSvalidate(m)

Arguments

m

an object of type ETS created with ETSforecast

Value

The same input object with the appropriate fields filled in, in particular:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

See Also

ETS, ETSforecast, ETSvalidate, ETScomponents

Examples

m1 <- ETSforecast(log(gdp))
m1 <- ETSvalidate(m1)

extract

Description

Reorder data frame returning column col reordered according to the values in column accordingTo

Usage

extract(x, col, accordingTo = 1)

Arguments

x

a data frame
col

column to be ordered
accordingTo

column to take as the pattern

Value

Data frame reordered accoring to a given column data

Author(s)

Diego J. Pedregal

gaussTest

Description

Gaussianity tests

Usage

gaussTest(y, runFromTests = FALSE)

Arguments

y

a vector, ts or tsibble object
runFromTests

internal check

Value

No return value, called for side effects

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

gaussTest(AirPassengers)

Spanish GDP

Description

Quarterly real Spanish Gross Domestic Product (gdp)

Usage

gdp

Format

Time series objects.

Quarterly since 1995

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Value

No return value, called for side effects

Examples

gdp

getp0

Description

Get initial conditions for parameters of UComp object

Usage

getp0(y, model = "llt/equal/arma(0,0)", periods = NA)

Arguments

y

a time series to forecast.
model

any valid UComp model without any ?.
periods

vector of fundamental period and harmonics required.

Details

Provides initial parameters of a given model for the time series. They may be changed arbitrarily by the user to include as an input p0 to UC or UCforecast functions (see example below). There is no guarantee that the model will converge and selecting initial conditions should be used with care.

Value

A set of parameters p0 of an object of class UComp to use as input to UC, UCforecast.

Author(s)

Diego J. Pedregal

See Also

UC, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents, UChp

Examples

## Not run: 
p0 <- getp0(log(AirPassengers), model = "llt/equal/arma(0,0)")
p0[1] <- 0  # p0[1] <- NA
m <- UCforecast(log(AirPassengers), model = "llt/equal/arma(0,0)", p0 = p0)

## End(Not run)

ident

Description

Autocorrelation functions of a time series

Usage

ident(y, nCoef = min(37, floor(length(y)/4)), nPar = 0, runFromTests = FALSE)

Arguments

y

a vector, ts or tsibble object
nCoef

number of autocorrelation coefficients to estimate
nPar

number of parameters in a model if y is a residual
runFromTests

internal check

Value

A vector with output table including ACF, etc.

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

ident(AirPassengers)

inv.box.cox

Description

Runs inverse of Box-Cox transform of a time series

Usage

inv.box.cox(x, lambda)

Arguments

x

Transformed time series object.
lambda

Lambda parameter used for Box-Cox transform.

Value

Inverse Box-Cox transformed time series

Author(s)

Diego J. Pedregal

See Also

box.cox, UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents

Examples

y <- inv.box.cox(box.cox(AirPassengers, 0.5), 0.5)
plot(y)

invBoxCox

Description

Calculates inverse of Box-Cox transformation with confidence bands, calculated as const time the standard error

Usage

invBoxCox(y, yVar, lambda, const = 2)

Arguments

y

matrix, array or vector
yVar

matrix, array or vector of variances of y
lambda

lambda parameter of Box-Cox transformation
const

number of standard error for confidence band

Value

Inverse of Box-Cox heteroskedasticity transformation with confidence bands

Author(s)

Diego J. Pedregal

Spanish Industrial Production Index

Description

Spanish Industrial Production Index (ipi).

Usage

ipi

Format

Objeto time series.

Monthly since 1975

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Value

No return value, called for side effects

Examples

ipi

OECD GDP

Description

Seasonally adjusted quarterly OECD real gross domestic product (OECDgdp).

Usage

OECDgdp

Format

Time series objects.

Quarterly data from 1962 to 2019

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Value

No return value, called for side effects

Examples

OECDgdp

plotAcfPacf

Description

Plot of ACF and PACF

Usage

plotAcfPacf(ACF, PACF, s = 1, n = NA, runFromTest = FALSE)

Arguments

ACF

variable to plot
PACF

second variable to plot
s

seasonal period
n

number of coefficients
runFromTest

internal check variable

Value

No return value, called for side effects

Author(s)

Diego J. Pedregal

plotBar

Description

Plot variable in bars

Usage

plotBar(ACF, s = 1, n = NA, label = "ACF")

Arguments

ACF

variable to plot
s

seasonal period
n

number of coefficients
label

label for plot

Value

Handle of plot

Author(s)

Diego J. Pedregal

plotSlide

Description

Plot summarised results from slide

Usage

plotSlide(py1, y, orig, step = 1, errorFun, collectFun = mean)

Arguments

py1

output from slide function
y

a vector, matrix or list of time series (the same used in slide call)
orig

starting forecasting origin (the same used in slide call)
step

observations ahead to move the forecasting origin (the same used in slide call)
errorFun

user function to calculate error measures
collectFun

aggregation function (mean, median, etc.)

Value

An array of forecasting errors of dimensions (horizon x nOrigs x nModels x nSeries)

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, Accuracy, tsDisplay, size

Examples

## Not run: plotSlide(py1, AirPassengers, 100, 1, errorFun)

plus_one

Description

Returns date of next to end time series y

Usage

plus_one(y)

Arguments

y

a ts object

Value

Next time stamp

Author(s)

Diego J. Pedregal

predict.UComp

Description

Forecasting using structural Unobseved Components models with prediction intervals

Usage

## S3 method for class 'UComp'
predict(object, newdata = NULL, n.ahead = NULL, level = 0.95, ...)

Arguments

object

Object of class “UComp”.
newdata

New output data to apply “UComp” object to.
n.ahead

Number of steps ahead to forecast or new inputs variables including their predictions.
level

Confidence level for prediction intervals.
...

Ignored.

Details

See help of UC.

Value

Forecasts of a UC model

A matrix with the mean forecasts and lower and upper prediction intervals

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents

Examples

y <- log(AirPassengers)
m1 <- UCforecast(y, model = "llt/eq/arma(0,0)")
f1 <- predict(m1)

removeNaNs

Description

Remove nans at beginning or end of vector

Usage

removeNaNs(x)

Arguments

x

a vector or a ts object

Value

vector with nans removed (only those at beginning or end)

Author(s)

Diego J. Pedregal

roots

Description

Roots of polynomial

Usage

roots(x)

Arguments

x

coefficients of polynomial in descending order

Value

Roots of polynomial

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

roots(c(1, -2 ,1))
roots(conv(c(1, -1), c(1, 0.8)))

rowMedians

Description

Medians of matrix by rows

Usage

rowMedians(x, na.rm = TRUE, ...)

Arguments

x

a matrix
na.rm

boolean indicating whether to remove nans
...

rest of inputs

Value

A vector with all the medians in rows

Author(s)

Diego J. Pedregal

See Also

colMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

s <- rowMedians(matrix(4, 3, 2))

Sales index for large retailers in Spain

Description

Sales index for food of large retailers in Spain

Usage

sales

Format

Time series objects.

Monthly data from January 1995 to December 2019

https://portal.mineco.gob.es/es-es/economiayempresa/EconomiaInformesMacro/Paginas/bdsice.aspx

Value

No return value, called for side effects

Examples

sales

size

Description

Size of vector, matrix or array

Usage

size(y)

Arguments

y

a vector, matrix or array

Value

A vector with all the dimensions

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay

Examples

s <- size(matrix(4, 3, 2))
s <- size(rep(4, 3))
s <- size(array(4, c(3, 2, 2)))

slide

Description

Rolling forecasting of a matrix of time series

Usage

slide(
  y,
  orig,
  forecFun,
  ...,
  h = 12,
  step = 1,
  output = TRUE,
  window = NA,
  parallel = FALSE
)

Arguments

y

a vector, a matrix or a list of time series
orig

starting forecasting origin
forecFun

user function that implements forecasting methods
...

rest of inputs to forecFun function
h

forecasting horizon
step

observations ahead to move the forecasting origin
output

output TRUE/FALSE
window

fixed window width in number of observations (NA for non fixed)
parallel

run forecasts in parallel

Details

Takes time series and run forecasting methods implemented in function forecFun h steps ahead along the time series y, starting at forecasting origin orig, and moving step observations ahead. Forecasts may be run in parallel by setting parallel to TRUE. A fixed window width may be specified with input window. The output is of dimensions (h, nOrigs, nModels, nSeries)

Value

An array of forecasts of dimensions (horizon x nOrigs x nModels x nSeries)

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, plotSlide, Accuracy, tsDisplay, size

Examples

## Not run: slide(AirPassengers, 100, forecFun)

slideAux

Description

Auxiliary function run from slide

Usage

slideAux(
  y,
  orig,
  forecFun,
  h = 12,
  step = 1,
  output = TRUE,
  graph = TRUE,
  window = NA,
  parallel = FALSE,
  isList = FALSE,
  ...
)

Arguments

y

a vector or matrix of time series
orig

starting forecasting origin
forecFun

user function that implements forecasting methods
h

forecasting horizon
step

observations ahead to move the forecasting origin
output

output TRUE/FALSE
graph

fraphical output TRUE/FALSE
window

fixed window width in number of observations (NA for non fixed)
parallel

run forecasts in parallel
isList

whether the input data y is a list or a matrix
...

rest of inputs to forecFun function

Value

Auxiliary output of slide function for just one time series

Author(s)

Diego J. Pedregal

sumStats

Description

Summary statistics of a matrix of variables

Usage

sumStats(y, decimals = 5)

Arguments

y

a vector, matrix of time series
decimals

number of decimals for table

Details

Position, dispersion, skewness, kurtosis, etc.

Value

Table of values in string matrix

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

s <- sumStats(AirPassengers)

tests

Description

Tests on a time series

Usage

tests(
  y,
  parts = 1/3,
  nCoef = min(25, length(x)/4),
  nPar = 0,
  s = frequency(y),
  avoid = 16
)

Arguments

y

a vector, ts or tsibble object
parts

proportion of sample to include in ratio of variances test
nCoef

number of autocorrelation coefficients to estimate
nPar

number of parameters in a model if y is a residual
s

seasonal period, number of observations per year
avoid

number of observations to avoid at beginning of sample to eliminate initial effects

Details

Multiple tests on a time series, including summary statistics, autocorrelation, Gaussianity and heteroskedasticity,

Value

Table with all test results

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

tests(AirPassengers)

TETS

Description

Runs all relevant functions for TETS modelling

Usage

TETS(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component with one or two letters:

  • Error: ? / A

  • Trend: ? / N / A / Ad

  • Seasonal: ? / N / A

s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
criterion

information criterion for identification ("aic", "bic" or "aicc").
forIntervals

estimate forecasting intervals (TRUE / FALSE)
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
verbose

intermediate estimation output (TRUE / FALSE)
alphaL

constraints limits for alpha parameter
betaL

constraints limits for beta parameter
gammaL

constraints limits for gamma parameter
phiL

constraints limits for phi parameter
p0

initial values for parameter search (alpha, beta, phi, gamma, sigma2) with consraints:
Ymin

scalar or vector of time varying censoring values from below
Ymax

scalar or vector of time varying censoring values from above

  • 0 < alpha < 1

  • 0 < beta < alpha

  • 0 < phi < 1

  • 0 < gamma < 1 - alpha

  • sigma2 > 0

Details

See help of TETSforecast.

Value

An object of class TETS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any TETS object as specified in what follows (function TETS fills in all of them at once):

After running TETSforecast:

p

Estimated parameters
criteria

Values for estimation criteria (LogLik, AIC, BIC, AICc)
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running TETSvalidate:

table

Estimation and validation table
comp

Estimated components in matrix form

After running TETScomponents:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

See Also

TETSforecast, TETSvalidate, TETScomponents

Examples

y <- log(AirPassengers)
m1 <- TETS(y)
m1 <- TETS(y, model = "MAM")

TETScomponents

Description

Estimates components of TOBIT TETS models

Usage

TETScomponents(m)

Arguments

m

an object of type TETS created with TETSforecast

Value

The same input object with the appropriate fields filled in, in particular:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

See Also

TETS, TETSforecast, TETSvalidate

Examples

m1 <- TETS(log(gdp))
m1 <- TETScomponents(m1)

TETSestim

Description

Estimates and forecasts TOBIT TETS models

Usage

TETSestim(m)

Arguments

m

an object of type TETS created with TETSforecast

Details

TETSestim estimates and forecasts a time series using an a TOBIT TETS model

Value

The same input object with the appropriate fields filled in, in particular:

p

Estimated parameters
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

Author(s)

Diego J. Pedregal

See Also

TETS, TETSforecast, TETSvalidate, TETScomponents

Examples

m1 <- TETSsetup(log(gdp))
m1 <- TETSestim(m1)

TETSforecast

Description

Estimates and forecasts TOBIT TETS general univariate models

Usage

TETSforecast(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = max(2 * s, 6),
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component with one or two letters:

  • Error: ? / A

  • Trend: ? / N / A / Ad

  • Seasonal: ? / N / A

s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
criterion

information criterion for identification ("aic", "bic" or "aicc").
forIntervals

estimate forecasting intervals (TRUE / FALSE)
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
verbose

intermediate estimation output (TRUE / FALSE)
alphaL

constraints limits for alpha parameter
betaL

constraints limits for beta parameter
gammaL

constraints limits for gamma parameter
phiL

constraints limits for phi parameter
p0

initial values for parameter search (alpha, beta, phi, gamma, sigma2) with consraints:
Ymin

scalar or vector of time varying censoring values from below
Ymax

scalar or vector of time varying censoring values from above

  • 0 < alpha < 1

  • 0 < beta < alpha

  • 0 < phi < 1

  • 0 < gamma < 1 - alpha

  • sigma2 > 0

Details

TETSforecast is a function for modelling and forecasting univariate time series with TOBIT ExponenTial Smoothing (TETS) time series models. It sets up the model with a number of control variables that govern the way the rest of functions in the package will work. It also estimates the model parameters by Maximum Likelihood and forecasts the data.

Value

An object of class TETS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any TETS object as specified in what follows (function TETS fills in all of them at once):

After running TETSforecast:

p

Estimated parameters
criteria

Values for estimation criteria (LogLik, AIC, BIC, AICc)
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running TETSvalidate:

table

Estimation and validation table
comp

Estimated components in matrix form

After running TETScomponents:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

See Also

TETS, TETSvalidate, TETScomponents

Examples

y <- log(AirPassengers)
m1 <- TETSforecast(y)
m1 <- TETSforecast(y, model = "A?A")

TETSsetup

Description

Sets up TOBIT TETS general univariate models

Usage

TETSsetup(
  y,
  u = NULL,
  model = "???",
  s = frequency(y),
  h = 2 * s,
  criterion = "aicc",
  forIntervals = FALSE,
  bootstrap = FALSE,
  nSimul = 5000,
  verbose = FALSE,
  alphaL = c(0, 1),
  betaL = alphaL,
  gammaL = alphaL,
  phiL = c(0.8, 0.98),
  p0 = -99999,
  Ymin = -Inf,
  Ymax = Inf
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input s should be supplied compulsorily (see below).
u

a matrix of input time series. If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component with one or two letters:

  • Error: ? / A

  • Trend: ? / N / A / Ad

  • Seasonal: ? / N / A

s

seasonal period of time series (1 for annual, 4 for quarterly, ...)
h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
criterion

information criterion for identification ("aic", "bic" or "aicc").
forIntervals

estimate forecasting intervals (TRUE / FALSE)
bootstrap

use bootstrap simulation for predictive distributions
nSimul

number of simulation runs for bootstrap simulation of predictive distributions
verbose

intermediate estimation output (TRUE / FALSE)
alphaL

constraints limits for alpha parameter
betaL

constraints limits for beta parameter
gammaL

constraints limits for gamma parameter
phiL

constraints limits for phi parameter
p0

initial values for parameter search (alpha, beta, phi, gamma, sigma2) with consraints:
Ymin

scalar or vector of time varying censoring values from below
Ymax

scalar or vector of time varying censoring values from above

  • 0 < alpha < 1

  • 0 < beta < alpha

  • 0 < phi < 1

  • 0 < gamma < 1 - alpha

  • sigma2 > 0

Details

See help of TETSforecast.

Value

An object of class TETS. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any TETS object as specified in what follows (function TETS fills in all of them at once):

After running TETSforecast:

p

Estimated parameters
criteria

Values for estimation criteria (LogLik, AIC, BIC, AICc)
yFor

Forecasted values of output
yForV

Variance of forecasted values of output
ySimul

Bootstrap simulations for forecasting distribution evaluation

After running TETSvalidate:

table

Estimation and validation table
comp

Estimated components in matrix form

After running TETScomponents:

comp

Estimated components in matrix form

Author(s)

Diego J. Pedregal

See Also

TETS, TETSforecast, TETSvalidate, TETScomponents

Examples

y <- log(AirPassengers)
m1 <- TETSsetup(y)
m1 <- TETSsetup(y,  model = "???")
m1 <- TETSsetup(y,  model = "?AA")

TETSvalidate

Description

Shows a table of estimation and diagnostics results for TOBIT TETS models

Usage

TETSvalidate(m)

Arguments

m

an object of type TETS created with TETSforecast

Value

The same input object with the appropriate fields filled in, in particular:

table

Estimation and validation table

Author(s)

Diego J. Pedregal

See Also

TETS, TETSforecast, TETSvalidate, TETScomponents

Examples

m1 <- TETSforecast(log(gdp))
m1 <- TETSvalidate(m1)

tsDisplay

Description

Displays time series plot with autocorrelation functions

Usage

tsDisplay(y, nCoef = 25, nPar = 0, s = NA)

Arguments

y

a vector, ts or tsibble object
nCoef

number of autocorrelation coefficients to estimate
nPar

number of parameters in a model if y is a residual
s

seasonal period, number of observations per year

Value

No return value, called for side effects

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, size

Examples

tsDisplay(AirPassengers)

UC

Description

Runs all relevant functions for UC modelling

Usage

UC(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 24,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = FALSE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input periods should be supplied compulsorily (see below).
u

a matrix of external regressors included only in the observation equation. (it may be either a numerical vector or a time series object). If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component. It allows two formats "trend/seasonal/irregular" or "trend/cycle/seasonal/irregular". The possibilities available for each component are:

  • Trend: ? / none / rw / irw / llt / dt / td;

  • Seasonal: ? / none / equal / different;

  • Irregular: ? / none / arma(0, 0) / arma(p, q) - with p and q integer positive orders;

  • Cycles: ? / none / combination of positive or negative numbers. Positive numbers fix the period of the cycle while negative values estimate the period taking as initial condition the absolute value of the period supplied. Several cycles with positive or negative values are possible and if a question mark is included, the model test for the existence of the cycles specified. The following are valid examples with different meanings: 48, 48?, -48, -48?, 48+60, -48+60, -48-60, 48-60, 48+60?, -48+60?, -48-60?, 48-60?.

h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
lambda

Box-Cox transformation lambda, NULL for automatic estimation
outlier

critical level of outlier tests. If NA it does not carry out any outlier detection (default). A positive value indicates the critical minimum t test for outlier detection in any model during identification. Three types of outliers are identified, namely Additive Outliers (AO), Level Shifts (LS) and Slope Change (SC).
tTest

augmented Dickey Fuller test for unit roots used in stepwise algorithm (TRUE / FALSE). The number of models to search for is reduced, depending on the result of this test.
criterion

information criterion for identification ("aic", "bic" or "aicc").
periods

vector of fundamental period and harmonics required.
verbose

intermediate results shown about progress of estimation (TRUE / FALSE).
stepwise

stepwise identification procedure (TRUE / FALSE).
p0

initial parameter vector for optimisation search.
arma

check for arma models for irregular components (TRUE / FALSE).
TVP

vector of zeros and ones to indicate TVP parameters.
trendOptions

trend models to select amongst (e.g., "rw/llt").
seasonalOptions

seasonal models to select amongst (e.g., "none/differentt").
irregularOptions

irregular models to select amongst (e.g., "none/arma(0,1)").

Details

UC is a function for modelling and forecasting univariate time series according to Unobserved Components models (UC). It sets up the model with a number of control variables that govern the way the rest of functions in the package work. It also estimates the model parameters by Maximum Likelihood, forecasts the data, performs smoothing, estimates model disturbances, estimates components and shows statistical diagnostics. Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Value

An object of class UComp. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any UComp object as specified in what follows (function UC fills in all of them at once):

After running UCforecast or UCestim:

  • p: Estimated parameters

  • v: Estimated innovations (white noise in correctly specified models)

  • yFor: Forecasted values of output

  • yForV: Forecasted values +- one standard error

  • criteria: Value of criteria for estimated model

  • iter: Number of iterations in estimation

  • grad: Gradient at estimated parameters

  • covp: Covariance matrix of parameters

After running UCvalidate:

  • table: Estimation and validation table

After running UCcomponents:

  • comp: Estimated components in matrix form

  • compV: Estimated components variance in matrix form

After running UCfilter, UCsmooth or UCdisturb:

  • yFit: Fitted values of output

  • yFitV: Variance of fitted values of output

  • a: State estimates

  • P: Variance of state estimates

  • aFor: Forecasts of states

  • PFor: Forecasts of states variances

After running UCdisturb:

  • eta: State perturbations estimates

  • eps: Observed perturbations estimates

Author(s)

Diego J. Pedregal

See Also

UC, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents, UChp

Examples

y <- log(AirPassengers)
m1 <- UC(y)
m1 <- UC(y, model = "llt/different/arma(0,0)")

UCcommand

Description

Auxiliar function for UC modeling

Usage

UCcommand(command, sys)

Arguments

command

Command to execute: "forecast", "validate", "filter", "smooth", "disturb", "components", "all"
sys

A UComp object created with UC

Value

The input UComp object with the appropriate fields filled in

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCcomponents, UCdisturb

Examples

cycle <- UChp(USgdp)
plot(cycle)

UCcomponents

Description

Estimates unobserved components of UC models Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Usage

UCcomponents(sys)

Arguments

sys

an object of type UComp created with UC or UCforecast

Value

The same input object with the appropriate fields filled in, in particular:

  • comp: Estimated components in matrix form

  • compV: Estimated components variance in matrix form

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCdisturb, UChp

Examples

m1 <- UC(log(AirPassengers))
m1 <- UCcomponents(m1)

UCdisturb

Description

Runs the Disturbance Smoother for UC models Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Usage

UCdisturb(sys)

Arguments

sys

an object of type UComp created with UC

Value

The same input object with the appropriate fields filled in, in particular:

  • yFit: Fitted values of output

  • yFitV: Variance of fitted values of output

  • a: State estimates

  • P: Variance of state estimates (diagonal of covariance matrices)

  • eta: State perturbations estimates

  • eps: Observed perturbations estimates

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCcomponents, UChp

Examples

m1 <- UC(log(AirPassengers))
m1 <- UCdisturb(m1)

UCestim

Description

Estimates and forecasts UC models

Usage

UCestim(sys)

Arguments

sys

an object of type UComp created with UC

Details

UCestim estimates and forecasts a time series using an UC model. The optimization method is a BFGS quasi-Newton algorithm with a backtracking line search using Armijo conditions. Parameter names in output table are the following:

  • Damping: Damping factor for DT trend.

  • Level: Variance of level disturbance.

  • Slope: Variance of slope disturbance.

  • Rho(#): Damping factor of cycle #.

  • Period(#): Estimated period of cycle #.

  • Var(#): Variance of cycle #.

  • Seas(#): Seasonal harmonic with period #.

  • Irregular: Variance of irregular component.

  • AR(#): AR parameter of lag #.

  • MA(#): MA parameter of lag #.

  • AO#: Additive outlier in observation #.

  • LS#: Level shift outlier in observation #.

  • SC#: Slope change outlier in observation #.

  • Beta(#): Beta parameter of input #.

  • Cnst: Constant.

Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Value

The same input object with the appropriate fields filled in, in particular:

  • p: Estimated transformed parameters

  • v: Estimated innovations (white noise in correctly specified models)

  • yFor: Forecast values of output

  • yForV: Forecasted values variance

  • criteria: Value of criteria for estimated model

  • covp: Covariance matrix of estimated transformed parameters

  • grad: Gradient of log-likelihood at the optimum

  • iter: Estimation iterations

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents, UChp

Examples

m1 <- UCsetup(log(AirPassengers))
m1 <- UCestim(m1)

UCfilter

Description

Runs the Kalman Filter for UC models Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Usage

UCfilter(sys)

Arguments

sys

an object of type UComp created with UC

Value

The same input object with the appropriate fields filled in, in particular:

  • yFit: Fitted values of output

  • yFitV: Variance of fitted values of output

  • a: State estimates

  • P: Variance of state estimates (diagonal of covariance matrices)

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCsmooth, UCdisturb, UCcomponents, UChp

Examples

m1 <- UC(log(AirPassengers))
m1 <- UCfilter(m1)

UCforecast

Description

Estimates and forecasts UC general univariate models

Usage

UCforecast(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 24,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = FALSE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input periods should be supplied compulsorily (see below).
u

a matrix of external regressors included only in the observation equation. (it may be either a numerical vector or a time series object). If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component. It allows two formats "trend/seasonal/irregular" or "trend/cycle/seasonal/irregular". The possibilities available for each component are:

  • Trend: ? / none / rw / irw / llt / dt / td;

  • Seasonal: ? / none / equal / different;

  • Irregular: ? / none / arma(0, 0) / arma(p, q) - with p and q integer positive orders;

  • Cycles: ? / none / combination of positive or negative numbers. Positive numbers fix the period of the cycle while negative values estimate the period taking as initial condition the absolute value of the period supplied. Several cycles with positive or negative values are possible and if a question mark is included, the model test for the existence of the cycles specified. The following are valid examples with different meanings: 48, 48?, -48, -48?, 48+60, -48+60, -48-60, 48-60, 48+60?, -48+60?, -48-60?, 48-60?.

h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
lambda

Box-Cox transformation lambda, NULL for automatic estimation
outlier

critical level of outlier tests. If NA it does not carry out any outlier detection (default). A positive value indicates the critical minimum t test for outlier detection in any model during identification. Three types of outliers are identified, namely Additive Outliers (AO), Level Shifts (LS) and Slope Change (SC).
tTest

augmented Dickey Fuller test for unit roots used in stepwise algorithm (TRUE / FALSE). The number of models to search for is reduced, depending on the result of this test.
criterion

information criterion for identification ("aic", "bic" or "aicc").
periods

vector of fundamental period and harmonics required.
verbose

intermediate results shown about progress of estimation (TRUE / FALSE).
stepwise

stepwise identification procedure (TRUE / FALSE).
p0

initial parameter vector for optimisation search.
arma

check for arma models for irregular components (TRUE / FALSE).
TVP

vector of zeros and ones to indicate TVP parameters.
trendOptions

trend models to select amongst (e.g., "rw/llt").
seasonalOptions

seasonal models to select amongst (e.g., "none/differentt").
irregularOptions

irregular models to select amongst (e.g., "none/arma(0,1)").

Details

UCforecast is a function for modelling and forecasting univariate time series according to Unobserved Components models (UC). It sets up the model with a number of control variables that govern the way the rest of functions in the package work. It also estimates the model parameters by Maximum Likelihood and forecasts the data. Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Value

An object of class UComp. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any UComp object as specified in what follows (function UC fills in all of them at once):

After running UCforecast:

  • p: Estimated parameters

  • v: Estimated innovations (white noise in correctly specified models)

  • yFor: Forecasted values of output

  • yForV: Forecasted values +- one standard error

  • criteria: Value of criteria for estimated model

  • iter: Number of iterations in estimation

  • grad: Gradient at estimated parameters

  • covp: Covariance matrix of parameters

After running UCvalidate:

  • table: Estimation and validation table

After running UCcomponents:

  • comp: Estimated components in matrix form

  • compV: Estimated components variance in matrix form

After running UCfilter, UCsmooth or UCdisturb:

  • yFit: Fitted values of output

  • yFitV: Variance of fitted values of output

  • a: State estimates

  • P: Variance of state estimates

  • aFor: Forecasts of states

  • PFor: Forecasts of states variances

After running UCdisturb:

  • eta: State perturbations estimates

  • eps: Observed perturbations estimates

Author(s)

Diego J. Pedregal

See Also

UC, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents, UChp

Examples

y <- log(AirPassengers)
m1 <- UCforecast(y)
m1 <- UCforecast(y, model = "llt/equal/arma(0,0)")

UChp

Description

Hodrick-Prescott filter estimation

Usage

UChp(y, lambda = 1600)

Arguments

y

A time series object
lambda

Smoothing constant (default: 1600)

Value

The cycle estimation

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCcomponents, UCdisturb

Examples

cycle <- UChp(USgdp)
plot(cycle)

UComp

Description

Package for time series modelling and forecasting of times series models inspired on different sources:

Details

  • Unobserved Components models due to A.C. Harvey (Basic Structural Model: BSM), enhanced with automatic identification tools by Diego J. Pedregal.

  • ExponenTial Smoothing by R.J. Hyndman and colaborators.

  • ARIMA models by V. Gómez and A. Maravall

  • Tobit ETS models by Pedregal, Trapero and Holgado

The package is designed for automatic identification among a wide range of possible models. The models may include exogenous variables. ARMA irregular components and automatic detection of outliers in some instances.

References

Harvey AC (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cam- bridge University Press.

de Jong, P & Penzer, J (1998). Diagnosing Shocks in Time Series, Journal of the American Statistical Association, 93, 442, 796-806.

Pedregal, DJ, & Young, PC (2002). Statistical approaches to modelling and forecasting time series. In M. Clements, & D. Hendry (Eds.), Companion to economic forecasting (pp. 69–104). Oxford: Blackwell Publishers.

Durbin J, Koopman SJ (2012). Time Series Analysis by State Space Methods. 38. Oxford University Press.

Proietti T and Luati A (2013). Maximum likelihood estimation of time series models: the Kalman filter and beyond, in Handbook of research methods and applications in empirical macroeconomics, ed. Nigar Hashimzade and Michael Thornton, E. Elgar, UK.

Hyndman RJ, Koehler AB, Ord JK and Snyder RD (2008), Forecasting with exponential smoothing, The State Sapce approach, Berlin, Springer-Verlag.

Gómez V and Maravall, A (2000), Automatic methods for univariate series. In Peña, D., Tiao, G.C. and Tsay R.S., A course in time series analyis. Wiley.

Trapero JR, Holgado E, Pedregal DJ (2024), Demand forecasting under lost sales stock policies, International Journal of Forecasting, 40, 1055-1068.

Maintainer

Diego J. Pedregal

Author(s)

Diego J. Pedregal

UCsetup

Description

Sets up UC general univariate models

Usage

UCsetup(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 24,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = FALSE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)

Arguments

y

a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input periods should be supplied compulsorily (see below).
u

a matrix of external regressors included only in the observation equation. (it may be either a numerical vector or a time series object). If the output wanted to be forecast, matrix u should contain future values for inputs.
model

the model to estimate. It is a single string indicating the type of model for each component. It allows two formats "trend/seasonal/irregular" or "trend/cycle/seasonal/irregular". The possibilities available for each component are:

  • Trend: ? / none / rw / irw / llt / dt / td;

  • Seasonal: ? / none / equal / different;

  • Irregular: ? / none / arma(0, 0) / arma(p, q) - with p and q integer positive orders;

  • Cycles: ? / none / combination of positive or negative numbers. Positive numbers fix the period of the cycle while negative values estimate the period taking as initial condition the absolute value of the period supplied. Several cycles with positive or negative values are possible and if a question mark is included, the model test for the existence of the cycles specified. The following are valid examples with different meanings: 48, 48?, -48, -48?, 48+60, -48+60, -48-60, 48-60, 48+60?, -48+60?, -48-60?, 48-60?.

h

forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.
lambda

Box-Cox transformation lambda, NULL for automatic estimation
outlier

critical level of outlier tests. If NA it does not carry out any outlier detection (default). A positive value indicates the critical minimum t test for outlier detection in any model during identification. Three types of outliers are identified, namely Additive Outliers (AO), Level Shifts (LS) and Slope Change (SC).
tTest

augmented Dickey Fuller test for unit roots used in stepwise algorithm (TRUE / FALSE). The number of models to search for is reduced, depending on the result of this test.
criterion

information criterion for identification ("aic", "bic" or "aicc").
periods

vector of fundamental period and harmonics required.
verbose

intermediate results shown about progress of estimation (TRUE / FALSE).
stepwise

stepwise identification procedure (TRUE / FALSE).
p0

initial parameter vector for optimisation search.
arma

check for arma models for irregular components (TRUE / FALSE).
TVP

vector of zeros and ones to indicate TVP parameters.
trendOptions

trend models to select amongst (e.g., "rw/llt").
seasonalOptions

seasonal models to select amongst (e.g., "none/differentt").
irregularOptions

irregular models to select amongst (e.g., "none/arma(0,1)").

Details

See help of UC.

Value

An object of class UComp. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any UComp object as specified in what follows (function UC fills in all of them at once):

After running UCforecast:

  • p: Estimated parameters

  • v: Estimated innovations (white noise in correctly specified models)

  • yFor: Forecasted values of output

  • yForV: Variance of forecasts

  • criteria: Value of criteria for estimated model

  • iter: Number of iterations in estimation

  • grad: Gradient at estimated parameters

  • covp: Covariance matrix of parameters

After running UCvalidate:

  • table: Estimation and validation table

After running UCcomponents:

  • comp: Estimated components in matrix form

  • compV: Estimated components variance in matrix form

After running UCfilter, UCsmooth or UCdisturb:

  • yFit: Fitted values of output

  • yFitV: Estimated fitted values variance

  • a: State estimates

  • P: Variance of state estimates

  • aFor: Forecasts of states

  • PFor: Forecasts of states variances

After running UCdisturb:

  • eta: State perturbations estimates

  • eps: Observed perturbations estimates

Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents, UChp

Examples

y <- log(AirPassengers)
m1 <- UCsetup(y)
m1 <- UCsetup(y, outlier = 4)
m1 <- UCsetup(y, model = "llt/equal/arma(0,0)")
m1 <- UCsetup(y, model = "?/?/?/?")
m1 <- UCsetup(y, model = "llt/?/equal/?", outlier = 4)

UCsmooth

Description

Runs the Fixed Interval Smoother for UC models Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Usage

UCsmooth(sys)

Arguments

sys

an object of type UComp created with UC

Value

The same input object with the appropriate fields filled in, in particular:

  • yFit: Fitted values of output

  • yFitV: Variance of fitted values of output

  • a: State estimates

  • P: Variance of state estimates (diagonal of covariance matrices)

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCvalidate, UCfilter, UCdisturb, UCcomponents, UChp

Examples

m1 <- UC(log(AirPassengers))
m1 <- UCsmooth(m1)

UCvalidate

Description

Shows a table of estimation and diagnostics results for UC models. Equivalent to print or summary. The table shows information in four sections: Firstly, information about the model estimated, the relevant periods of the seasonal component included, and further information about convergence. Secondly, parameters with their names are provided, the asymptotic standard errors, the ratio of the two, and the gradient at the optimum. One asterisk indicates concentrated-out parameters and two asterisks signals parameters constrained during estimation. Thirdly, information criteria and the value of the log-likelihood. Finally, diagnostic statistics about innovations, namely, the Ljung-Box Q test of absense of autocorrelation statistic for several lags, the Jarque-Bera gaussianity test, and a standard ratio of variances test.

Usage

UCvalidate(sys, printScreen = TRUE)

Arguments

sys

an object of type UComp created with UC
printScreen

print to screen or just return output table

Value

The same input object with the appropriate fields filled in, in particular:

  • table: Estimation and validation table

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCfilter, UCsmooth, UCdisturb, UCcomponents, UChp

Examples

m1 <- UC(log(gdp))
m1 <- UCvalidate(m1)

US GDP

Description

Seasonally adjusted quarterly US real gross domestic product (USgdp).

Usage

USgdp

Format

Time series objects.

Quarterly data from 1962 to 2019

Value

No return value, called for side effects

Source

USgdp

Examples

USgdp

varTest

Description

Ratio of variances test

Usage

varTest(y, parts = 1/3)

Arguments

y

a vector, ts or tsibble object
parts

portion of sample to estimate variances

Value

Table with test results

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, conv, armaFilter, dif, roots, zplane, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

varTest(AirPassengers)

WEEKforecast

Description

Estimates and forecasts weekly time series with monthly and annual seasonal patterns

Usage

WEEKforecast(
  y,
  u = NULL,
  initial_date,
  h = 24,
  lambda = 1,
  criterion = "aic",
  p0 = -9999.9,
  verbose = FALSE
)

Arguments

y

A numeric vector, ts object or list containing weekly observations of the dependent variable.
u

Optional matrix or vector of exogenous regressors. If provided, it must cover both the estimation and forecast periods.
initial_date

A character or Date object indicating the calendar start date of the series.
h

Integer indicating the forecast horizon (number of weeks ahead).
lambda

Box–Cox transformation parameter.
criterion

Information criterion used for model selection (AIC, BIC or AICc).
p0

Initial parameter vector for Maximum Likelihood estimation.
verbose

if TRUE, prints estimation details.

Details

WEEKforecast estimates and forecasts univariate weekly time series using Dynamic Harmonic Regression (DHR).

The function is designed for weekly data but builds the seasonal structure from underlying daily calendar information. In particular, it incorporates:

  • Monthly seasonality via harmonic terms derived from calendar months

  • Annual seasonality via multiple harmonic components based on calendar years

Standard methods applicable to UComp objects are available.

Value

An object of class UComp. It is a list containing the model specification, estimated parameters, and forecasting results.

Author(s)

Diego J. Pedregal

See Also

UC, UCforecast, UCfilter, UCsmooth, UCdisturb, UCcomponents

Examples

y <- rnorm(400)
m <- WEEKforecast(y, initial_date = "2015-01-01", h = 12)

zplane

Description

Real-imaginary plane to show roots of digital filters (ARMA)

Usage

zplane(MApoly = 1, ARpoly = 1)

Arguments

MApoly

coefficients of numerator polynomial in descending order
ARpoly

coefficients of denominator polynomial in descending order

Details

Shows the real-imaginary plane to show zeros (roots of numerator or MA polynomial) and poles (roots of denominator of AR polynomial). Unit roots and real vs imaginary roots can be seen by eye

Value

No return value, called for side effects

Author(s)

Diego J. Pedregal

See Also

colMedians, rowMedians, tests, sumStats, gaussTest, ident, cusum, varTest, conv, armaFilter, dif, roots, acft, slide, plotSlide, Accuracy, tsDisplay, size

Examples

zplane(c(1, -2, 1), c(1, -0.8))