Transfer Function and ARIMA Models.

Description

The tfarima package provides classes and methods to build customized transfer function and ARIMA models with multiple operators and parameter restrictions. The package also includes functions for model identification, model estimation (exact or conditional maximum likelihood), model diagnostic checking, automatic outlier detection, calendar effects, forecasting and seasonal adjustment.

Author(s)

Jose Luis Gallego jose.gallego@unican.es

References

Bell, W.R. and Hillmer, S.C. (1983) Modeling Time Series with Calendar Variation, Journal of the American Statistical Association, Vol. 78, No. 383, pp. 526-534.

Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015) Time Series Analysis: Forecasting and Control. John Wiley & Sons, Hoboken.

Box, G.E.P., Pierce, D.A. and Newbold, D. A. (1987) Estimating Trend and Growth Rates in Seasonal Time Series, Journal of the American Statistical Association, Vol. 82, No. 397, pp. 276-282.

Box, G.E.P. and Tiao, G.C. (1975) “Intervention Analysis with Applications to Economic and Environmental Problems”, Journal of the American Statistical Association, Vol. 70, No. 349, pp. 70-79.

Chen, C. and Liu, L. (1993) Joint Estimation of Model Parameters and Outlier Effects in Time Series, Journal of the American Statistical Association, Vol. 88, No. 421, pp. 284-297

Thompson, H. E. and Tiao, G. C. (1971) "Analysis of Telephone Data: A Case Study of Forecasting Seasonal Time Series," Bell Journal of Economics, The RAND Corporation, vol. 2(2), pages 515-541, Autumn.

Calendar variables

Description

CalendarVar creates a set of deterministic variables to capture calendar effects.

Usage

CalendarVar(
  x,
  form = c("dif", "td", "td7", "td6", "wd", "wd2", "null"),
  ref = 0,
  lom = TRUE,
  lpyear = TRUE,
  easter = FALSE,
  len = 4,
  easter.mon = FALSE,
  n.ahead = 0
)

Arguments

Value

An object of class mts or ts.

References

Bell, W.R. and Hillmer, S.C. (1983) “Modeling time series with calendar variation”, Journal of the American Statistical Society, Vol. 78, pp. 526–534.

Examples

Y <- rsales
X <- CalendarVar(Y, easter = TRUE)

Intervention variables

Description

InterventionVar creates an intervention variable to capture the effect of an external event.

Usage

InterventionVar(Y, date, type = c("P", "S", "R"), n.ahead = 0)

Arguments

Value

An intervention variable, a 'ts' object.

References

G. E. P. Box, G. C. Tiao, “Intervention Analysis with Applications to Economic and Environmental Problems”, Journal of the American Statistical Association, Vol. 70, No. 349. (Mar., 1975), pp. 70-79.

Examples

Y <- seriesJ$Y
P58 <- InterventionVar(Y, date = 58, type = "P")

Annual sum

Description

S generates the annual sum of a monthly or quarterly time series.

Usage

S(x, extend = TRUE)

Arguments

Value

The transformed time series, a ts object.

Wisconsin Telephone Company

Description

Monthly data from January 1951 to October 1966.

Usage

Wtelephone

Format

A object of class data.frame with 215 rows and 2 columns:

X

Monthly outward station movements.

Y

Montly inward station movements.

Source

https://drive.google.com/file/d/1LP8aMIQewMrxgOlrg9rN3eWHhZuUsY8K/view?usp=sharing

References

Thompson, H. E. and Tiao, G. C. (1971) "Analysis of Telephone Data: A Case Study of Forecasting Seasonal Time Series," Bell Journal of Economics, The RAND Corporation, vol. 2(2), pages 515-541, Autumn.

Lag polynomial

Description

as.lagpol converts a numeric vector c(1, -a_1, ..., -a_d) into a lag polynomial (1 - a_1 B - ... - a_p B^p).

Usage

as.lagpol(pol, p = 1)

Arguments

Value

An object of class lagpol.

Examples

as.lagpol(c(1, -0.8))
as.lagpol(c(1, 0, 0, 0, -0.8))

Convert arima into um.

Description

as.um converts an object of class arima into an object of class um.

Usage

as.um(arima)

Arguments

Value

An object of class um.

Examples

z <- AirPassengers
a <- arima(log(z), order = c(0,1,1), 
seasonal = list(order = c(0,1,1), frequency = 12))
um1 <- as.um(a)

Theoretical simple/partial autocorrelations of an ARMA model

Description

autocorr computes the simple/partial autocorrelations of an ARMA model.

Usage

autocorr(um, ...)

## S3 method for class 'um'
autocorr(um, lag.max = 10, par = FALSE, ...)

Arguments

Value

A numeric vector.

Note

The I polynomial is ignored.

Examples

ar1 <- um(ar = "1-0.8B")
autocorr(ar1, lag.max = 13)
autocorr(ar1, lag.max = 13, par = TRUE)

Theoretical autocovariances of an ARMA model

Description

autocov computes the autocovariances of an ARMA model.

Usage

## S3 method for class 'stsm'
autocov(mdl, ...)

autocov(mdl, ...)

## S3 method for class 'um'
autocov(mdl, lag.max = 10, ...)

Arguments

Value

A numeric vector.

Note

The I polynomial is ignored.

Examples

# Local level model
b <- 1
C <- as.matrix(1)
stsm1 <- stsm(b = b, C = C, s2v = c(lvl = 1469.619), s2u = c(irr = 15103.061))
autocov(stsm1)

ar1 <- um(ar = "1-0.8B")
autocov(ar1, lag.max = 13)

Basic Structural Time Series models

Description

bsm creates/estimates basic structural models for seasonal time series.

Usage

bsm(
  y,
  bc = FALSE,
  seas = c("hd", "ht", "hs"),
  s2v = c(lvl = 0.2, slp = 0.05, seas = 0.075),
  s2u = 0.1,
  xreg = NULL,
  fSv = NULL,
  ...
)

Arguments

Value

An object of class stsm.

References

Durbin, J. and Koopman, S.J. (2012) Time Series Analysis by State Space Methods, 2nd ed., Oxford University Press, Oxford.

Examples

bsm1 <- bsm(AirPassengers, bc = TRUE)

Calendar effects

Description

calendar extends the ARIMA model um by including a set of deterministic variables to capture the calendar variation in a monthly time series. Two equivalent representations are available: (i) D0, D1, ..., D6, (ii) L, D1-D0, ..., D6-D0 where D0, D2, ..., D6 are deterministic variables representing the number of Sundays, Mondays, ..., Saturdays, L = D0 + D1 + ... + D6 is the of the month. Alternatively, the Leap Year indicator (LPY) can be included instead of L. The seven trading days can also be compacted into two variables: week days and weekends. Optionally, a deterministic variable to estimate the Easter effect can also be included, see "easter".

Usage

## S3 method for class 'tfm'
calendar(
  mdl,
  y = NULL,
  form = c("dif", "td", "td7", "td6", "wd"),
  ref = 0,
  lom = TRUE,
  lpyear = TRUE,
  easter = FALSE,
  len = 4,
  easter.mon = FALSE,
  n.ahead = 0,
  p.value = 1,
  envir = NULL,
  ...
)

calendar(mdl, ...)

## S3 method for class 'um'
calendar(
  mdl,
  y = NULL,
  form = c("dif", "td", "td7", "td6", "wd"),
  ref = 0,
  lom = TRUE,
  lpyear = TRUE,
  easter = FALSE,
  len = 4,
  easter.mon = FALSE,
  n.ahead = 0,
  p.value = 1,
  envir = NULL,
  ...
)

Arguments

Value

An object of class "tfm".

References

W. R. Bell & S. C. Hillmer (1983) Modeling Time Series with Calendar Variation, Journal of the American Statistical Association, 78:383, 526-534, DOI: 10.1080/01621459.1983.10478005

Examples

Y <- tfarima::rsales
um1 <- um(Y, i = list(1, c(1, 12)), ma = list(1, c(1, 12)), bc = TRUE)
tfm1 <- calendar(um1)

Cross-correlation check

Description

ccf displays ccf between prewhitened inputs and residuals.

Usage

ccf.tfm(tfm, lag.max = NULL, method = c("exact", "cond"), envir = NULL, ...)

Arguments

Coefficients of a transfer function model

Description

coef extracts the "coefficients" from a TF model.

Usage

## S3 method for class 'tfm'
coef(object, ...)

Arguments

Value

A numeric vector.

Coefficients of a univariate model

Description

coef extracts the "coefficients" from a um object.

Usage

## S3 method for class 'um'
coef(object, ...)

Arguments

Value

A numeric vector.

Diagnostic checking

Description

diagchk displays tools for diagnostic checking.

Usage

## S3 method for class 'tfm'
diagchk(
  mdl,
  y = NULL,
  method = c("exact", "cond"),
  lag.max = NULL,
  lags.at = NULL,
  freq.at = NULL,
  std = TRUE,
  envir = NULL,
  ...
)

diagchk(mdl, ...)

## S3 method for class 'um'
diagchk(
  mdl,
  z = NULL,
  method = c("exact", "cond"),
  lag.max = NULL,
  lags.at = NULL,
  freq.at = NULL,
  std = TRUE,
  envir = NULL,
  ...
)

Arguments

Examples

z <- AirPassengers
airl <- um(z, i = list(1, c(1,12)), ma = list(1, c(1,12)), bc = TRUE)
diagchk(airl)

Graphs for ARMA models

Description

display shows graphs characterizing one or a list of ARMA models.

Usage

display(um, ...)

## S3 method for class 'um'
display(
  um,
  lag.max = 25,
  n.freq = 501,
  log.spec = FALSE,
  graphs = c("acf", "pacf", "spec"),
  byrow = FALSE,
  eq = TRUE,
  ...
)

## Default S3 method:
display(um, ...)

Arguments

Examples

um1 <- um(ar = "(1 - 0.8B)(1 - 0.8B^12)")
um2 <- um(ma = "(1 - 0.8B)(1 - 0.8B^12)")
display(list(um1, um2))

Easter effect

Description

easter extends the ARIMA model um by including a regression variable to capture the Easter effect.

Usage

easter(um, ...)

## S3 method for class 'um'
easter(
  um,
  z = NULL,
  len = 4,
  easter.mon = FALSE,
  n.ahead = 0,
  envir = NULL,
  ...
)

Arguments

Value

An object of class "tfm".

Examples

Y <- rsales
um1 <- um(Y, i = list(1, c(1, 12)), ma = list(1, c(1, 12)), bc = TRUE)
tfm1 <- easter(um1)

Estimation of a STS model

Description

fit fits the stsm to the time series y.

Usage

## S3 method for class 'stsm'
fit(mdl, method = "BFGS", show.iter = FALSE, ...)

Arguments

Value

An object of class "stsm" with the estimated variances.

Examples

# Local level model
b <- 1
C <- as.matrix(1)
stsm1 <- stsm(Nile, b, C, s2v = c(lvl = 0.5), s2u = c(irr = 1), fit = FALSE)
stsm1 <- fit(stsm1, method = "L-BFGS-B")

Estimation of the ARIMA model

Description

fit fits the univariate model to the time series z.

Usage

## S3 method for class 'tfm'
fit(
  mdl,
  y = NULL,
  method = c("exact", "cond"),
  optim.method = "BFGS",
  show.iter = FALSE,
  fit.noise = TRUE,
  envir = NULL,
  ...
)

fit(mdl, ...)

## S3 method for class 'um'
fit(
  mdl,
  z = NULL,
  method = c("exact", "cond"),
  optim.method = "BFGS",
  show.iter = FALSE,
  envir = NULL,
  ...
)

Arguments

Value

A tfm object.

An object of class "um" with the estimated parameters.

Note

The um function estimates the corresponding ARIMA model when a time series is provided. The fit function is useful to fit a model to several time series, for example, in a Monte Carlo study.

Examples

z <- AirPassengers
airl <- um(i = list(1, c(1, 12)), ma = list(1, c(1, 12)), bc = TRUE)
airl <- fit(airl, z)

Estimation of a STS model by the method of moments

Description

fit2autocov fits a STS model to a vector of theoretical autocovariances.

Usage

fit2autocov(mdl, ...)

## S3 method for class 'stsm'
fit2autocov(mdl, g, method = "BFGS", show.iter = FALSE, ...)

Arguments

Value

An object of class stsm.

Examples

um1 <- um(Nile, i = 1, ma = 1)
g <- autocov(um1, lag.max = 1)
# Local level model
b <- 1
C <- as.matrix(1)
stsm1 <- stsm(Nile, b, C, s2v = c(lvl = 0.5), s2u = c(irr = 1), fit = FALSE)
stsm2 <- fit2autocov(stsm1, g)
stsm2

Identification plots

Description

ide displays graphs useful to identify a tentative ARIMA model for a time series.

Usage

ide(
  Y,
  transf = list(),
  order.polreg = 0,
  lag.max = NULL,
  lags.at = NULL,
  freq.at = NULL,
  wn.bands = TRUE,
  graphs = c("plot", "acf", "pacf"),
  set.layout = TRUE,
  byrow = TRUE,
  main = "",
  envir = NULL,
  ...
)

Arguments

Examples

Y <- AirPassengers
ide(Y, graphs = c("plot", "rm"))
ide(Y, transf = list(list(bc = TRUE, S = TRUE), list(bc = TRUE, d = 1, D = 1)))

Intervention analysis/Outlier treatment

Description

intervention estimates the effect of a intervention at a known time.

Usage

## S3 method for class 'tfm'
intervention(
  mdl,
  y = NULL,
  type,
  time,
  n.ahead = 0,
  envir = parent.frame(),
  ...
)

intervention(mdl, ...)

## S3 method for class 'um'
intervention(
  mdl,
  y = NULL,
  type,
  time,
  n.ahead = 0,
  envir = parent.frame(),
  ...
)

Arguments

Value

an object of class "tfm" or a table.

Inverse of a lag polynomial

Description

inv inverts a lag polynomial until the indicated lag.

Usage

inv(lp, ...)

## S3 method for class 'lagpol'
inv(lp, lag.max = 10, ...)

Arguments

Value

inv returns a numeric vector with the coefficients of the inverse lag polynomial truncated at lag.max.

Examples

inv(as.lagpol(c(1, 1.2, -0.8))) 

Lag polynomials

Description

lagpol creates a lag polynomial of the form (1 - coef_1 B^s - ... - coef_d B^sd)^p. This class of lag polynomials is defined by a vector of d coefficients c(coef_1, ..., coef_d), the powers s and p, and a vector of k parameters c(param_1, ..., param_k). The vector c(coef_1, ..., coef_d) is actually a vector of math expressions to compute the value of each coefficient in terms of the parameters.

Usage

lagpol(param = NULL, s = 1, p = 1, lags = NULL, coef = NULL)

Arguments

Value

lagpol returns an object of class "lagpol" with the following components:

coef

Vector of coefficients c(coef_1, ..., coef_p) provided to create the lag polynomial.

pol

Base lag polynomial, c(1, -coef_1, ..., -coef_d).

Pol

Power lag polynomial when p > 1.

Examples

lagpol(param = c(phi = 0.8) )
lagpol(param = c(phi1 = 1.2, phi2 = -0.6), s = 4)
lagpol(param = c(delta = 1), p = 2)

Log-likelihood of an ARIMA model

Description

logLik computes the exact or conditional log-likelihood of object of the class um.

Usage

## S3 method for class 'um'
logLik(object, z = NULL, method = c("exact", "cond"), ...)

Arguments

Value

The exact or conditional log-likelihood.

Modifying a TF or an ARIMA model

Description

modify modifies an object of class um or tfm by adding and/or removing lag polynomials.

Usage

## S3 method for class 'tfm'
modify(mdl, ...)

modify(mdl, ...)

## S3 method for class 'um'
modify(
  mdl,
  ar = NULL,
  i = NULL,
  ma = NULL,
  mu = NULL,
  sig2 = NULL,
  bc = NULL,
  fit = TRUE,
  ...
)

Arguments

Value

An object of class um or um.

Examples

um1 <- um(ar = "(1 - 0.8B)")
um2 <- modify(um1, ar = list(0, "(1 - 0.9B)"), ma = "(1 - 0.5B)")

Unscramble I polynomial

Description

nabla multiplies the I polynomials of an object of the um class.

Usage

nabla(um)

## S3 method for class 'um'
nabla(um)

Arguments

Value

A numeric vector c(1, a1, ..., ad)

Note

This function returns the member variable um$nabla.

Examples

um1 <- um(i = "(1 - B)(1 - B^12)")
nabla(um1)

Noise of a transfer function model

Description

noise computes the noise of a linear transfer function model.

Usage

noise(tfm, ...)

## S3 method for class 'tfm'
noise(tfm, y = NULL, diff = TRUE, exp = FALSE, envir = NULL, ...)

Arguments

Value

A "ts" object.

Outlier dates

Description

outlierDates shows the indeces and dates of outliers.

Usage

outlierDates(x, c = 3)

Arguments

Value

A table with the indices, dates and z-scores of the outliers.

Outliers detection at known/unknown dates

Description

outliers performs a detection of four types of anomalies (AO, TC, LS and IO) in a time series described by an ARIMA model. If the dates of the outliers are unknown, an iterative detection process like that proposed by Chen and Liu (1993) is conducted.

Usage

## S3 method for class 'tfm'
outliers(
  mdl,
  y = NULL,
  types = c("AO", "LS", "TC", "IO"),
  dates = NULL,
  c = 3,
  calendar = FALSE,
  easter = FALSE,
  resid = c("exact", "cond"),
  n.ahead = NULL,
  p.value = 1,
  tc.fix = TRUE,
  envir = NULL,
  ...
)

outliers(mdl, ...)

## S3 method for class 'um'
outliers(
  mdl,
  y = NULL,
  types = c("AO", "LS", "TC", "IO"),
  dates = NULL,
  c = 3,
  calendar = FALSE,
  easter = FALSE,
  resid = c("exact", "cond"),
  n.ahead = 0,
  p.value = 1,
  tc.fix = TRUE,
  envir = NULL,
  ...
)

Arguments

Value

an object of class "tfm" or a table.

Examples

Y <- rsales
um1 <- um(Y, i = list(1, c(1, 12)), ma = list(1, c(1, 12)), bc = TRUE)
outliers(um1)

Output of a transfer function

Description

output filters the input using the transfer function.

Usage

output.tf(tf)

Arguments

Value

A "ts" object

Prewhitened cross correlation function

Description

pccf displays cross correlation function between input and output after prewhitening both through a univariate model.

Usage

pccf(
  x,
  y,
  um.x = NULL,
  um.y = NULL,
  lag.max = NULL,
  plot = TRUE,
  envir = NULL,
  main = NULL,
  nu.weights = FALSE,
  ...
)

Arguments

Value

The estimated cross correlations are displayed in a graph or returned into a numeric vector.

Unscramble AR polynomial

Description

phi multiplies the AR polynomials of an object of the um class.

Usage

phi(um)

## S3 method for class 'um'
phi(um)

Arguments

Value

A numeric vector c(1, a1, ..., ad)

Note

This function returns the member variable um$phi.

Examples

um1 <- um(ar = "(1 - 0.8B)(1 - 0.5B)")
phi(um1)

Pi weights of an AR(I)MA model

Description

pi.weights computes the pi-weights of an AR(I)MA model.

Usage

pi.weights(um, ...)

## S3 method for class 'um'
pi.weights(um, lag.max = 10, var.pi = FALSE, ...)

Arguments

Value

A numeric vector.

Examples

um1 <- um(i = "(1 - B)(1 - B^12)", ma = "(1 - 0.8B)(1 - 0.8B^12)")
pi.weights(um1, var.pi = TRUE)

Forecasting with transfer function models

Description

predict computes point and interval predictions for a time series based on a tfm object.

Usage

## S3 method for class 'tfm'
predict(
  object,
  newdata = NULL,
  y = NULL,
  ori = NULL,
  n.ahead = NULL,
  level = 0.95,
  i = NULL,
  envir = NULL,
  ...
)

Arguments

Details

Forecasts for the inputs of a tfm object can be provided in tree ways: (1) extending the time series with forecasts so that the length of the intput is greater than the length of the output, (2) computed internally from the um object associated to the input and (3) with the newdata argument.

Forecasts from an ARIMA model

Description

predict computes point and interval predictions for a time series from models of class um.

Usage

## S3 method for class 'um'
predict(
  object,
  z = NULL,
  ori = NULL,
  n.ahead = 1,
  level = 0.95,
  i = NULL,
  envir = NULL,
  ...
)

Arguments

Value

An object of class "tfm".

Examples

Z <- AirPassengers
um1 <- um(Z, i = list(1, c(1, 12)), ma = list(1, c(1, 12)), bc = TRUE)
p <- predict(um1, n.ahead = 12)
p
plot(p, n.back = 60)

Print numeric vector as a lagpol object

Description

Print numeric vector as a lagpol object

Usage

printLagpol(pol, digits = 2)

Arguments

Print a list of lagpol objects

Description

Print a list of lagpol objects

Usage

printLagpolList(llp, digits = 2)

Arguments

Psi weights of an AR(I)MA model

Description

psi computes the psi-weights of an AR(I)MA model.

Usage

psi.weights(um, ...)

## S3 method for class 'um'
psi.weights(um, lag.max = 10, var.psi = FALSE, ...)

Arguments

Value

A numeric vector.

Examples

um1 <- um(i = "(1 - B)(1 - B^12)", ma = "(1 - 0.8B)(1 - 0.8B^12)")
psi.weights(um1)
psi.weights(um1, var.psi = TRUE)

Residuals of a transfer function model

Description

residuals computes the exact or conditional residuals of a TF model.

Usage

## S3 method for class 'tfm'
residuals(object, y = NULL, method = c("exact", "cond"), envir = NULL, ...)

Arguments

Value

A "ts" object.

Residuals of the ARIMA model

Description

residuals computes the exact or conditional residuals.

Usage

## S3 method for class 'um'
residuals(object, z = NULL, method = c("exact", "cond"), envir = NULL, ...)

Arguments

Value

An object of class um.

Examples

z <- AirPassengers
airl <- um(z, i = list(1, c(1, 12)), ma = list(1, c(1, 12)), bc = TRUE)
r <- residuals(airl)
summary(r)

Reduce form for STS model

Description

rform finds the reduce form for a STS model.

Usage

rform(mdl, ...)

## S3 method for class 'stsm'
rform(mdl, ...)

Arguments

Value

An object of class um.

Examples

b <- 1
C <- as.matrix(1)
stsm1 <- stsm(b = b, C = C, s2v = c(lvl = 1469.619), s2u = c(irr = 15103.061))
rf1 <- rform(stsm1)
nabla(rf1)
theta(rf1)

Roots of the lag polynomials of an ARIMA model

Description

roots compute the roots of the AR, I, MA lag polynomials an ARIMA model.

Usage

roots(x, ...)

## S3 method for class 'um'
roots(x, opr = c("arma", "ar", "ma", "i", "arima"), ...)

Arguments

Value

List of matrices with the roots of each single polynomial.

Examples

um1 <- um(ar = "(1 - 0.8B)(1 - 0.8B^12)")
roots(um1)

Roots of a lag polynomial

Description

roots.lagpol computes the roots of a lag polynomial.

Usage

## S3 method for class 'lagpol'
roots(x, table = TRUE, ...)

## Default S3 method:
roots(x, ...)

Arguments

Value

A vector or a table.

Examples

roots(c(1, 1.2, -0.8))

Retail Sales of Variety Stores (U.S. Bureau of the Census)

Description

156 monthly observations from January 1967 to December 1979.

Usage

rsales

Format

An object of class ts of length 156.

References

Chen, C. and Liu, L. (1993) Joint Estimation of Model Parameters and Outlier Effects in Time Series, Journal of the American Statistical Association, Vol. 88, No. 421, pp. 284-297

Seasonal dummies

Description

sdummies creates an full set of seasonal dummies.

Usage

sdummies(Y, ref = 1, constant = FALSE, n.ahead = 0)

Arguments

Value

A matrix of trigonometric variables.

Examples

Y <- AirPassengers
P58 <- sincos(Y)

Seasonal adjustment

Description

seasadj removes the seasonal component of time series.

Usage

seasadj(mdl, ...)

## S3 method for class 'um'
seasadj(
  mdl,
  z = NULL,
  method = c("mixed", "forecast", "backcast"),
  envir = NULL,
  ...
)

Arguments

Value

seasadj returns a seasonal adjusted time series.

Examples

Y <- AirPassengers
um1 <- um(Y, bc = TRUE, i = list(1, c(1,12)), ma = list(1, c(1,12)))
Y <- seasadj(um1)
ide(Y)

Series C Chemical Process Temperature Readings: Every Minute.

Description

226 observations.

Usage

seriesC

Format

An object of class numeric of length 226.

References

Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015) Time Series Analysis: Forecasting and Control. John Wiley & Sons, Hoboken.

Gas furnace data

Description

Sampling interval 9 seconds; observations for 296 pairs of data points.

Usage

seriesJ

Format

A object of class data.frame with 296 rows and 2 columns:

X

0.60-0.04 (input gas rate in cubir feet per minute.)

Y

% CO2 in outlet gas.

References

Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015) Time Series Analysis: Forecasting and Control. John Wiley & Sons, Hoboken.

setinputs adds new inputs into a transfer function model.

Description

setinputs adds new inputs into a transfer function model.

Usage

## S3 method for class 'tfm'
setinputs(
  mdl,
  xreg = NULL,
  inputs = NULL,
  y = NULL,
  envir = parent.frame(),
  ...
)

setinputs(mdl, ...)

## S3 method for class 'um'
setinputs(mdl, xreg = NULL, inputs = NULL, y = NULL, envir = NULL, ...)

Arguments

Value

A tfm object.

Structural form for an ARIMA model

Description

sform finds the structural form for an ARIMA model from its the eventual forecast function.

Usage

sform(mdl, ...)

## S3 method for class 'um'
sform(mdl, fSv = NULL, par = NULL, ...)

Arguments

Value

An object of class stsm

Examples

airl <- um(i = list(1, c(1, 12)), ma = "(1 - 0.86B)(1 - 0.8B12)")
sf <- sform(airl)
sf

Signal component of a TF model

Description

signal extracts the signal of a TF model.

Usage

signal(mdl, ...)

## S3 method for class 'tfm'
signal(mdl, y = NULL, diff = TRUE, envir = NULL, ...)

Arguments

Value

A "ts" object.

Time series simulation form an ARIMA or TF model

Description

sim generates a random time series from an object of class um or tfm.

Usage

## S3 method for class 'tfm'
sim(mdl, n = 100, y0 = NULL, seed = NULL, ...)

sim(mdl, ...)

## S3 method for class 'um'
sim(
  mdl,
  n = 100,
  z0 = NULL,
  n0 = 0,
  a = NULL,
  seed = NULL,
  envir = parent.frame(),
  ...
)

Arguments

Value

An object of class ts.

Trigonometric variables

Description

sincos creates an full set of trigonometric variables.

Usage

sincos(Y, n.ahead = 0, constant = FALSE)

Arguments

Value

A matrix of trigonometric variables.

Examples

Y <- AirPassengers
P58 <- sincos(Y)

Spectrum of an ARMA model

Description

spec computes the spectrum of an ARMA model.

Usage

spec(um, ...)

## S3 method for class 'um'
spec(um, n.freq = 501, ...)

Arguments

Value

A matrix with the frequencies and the power spectral densities.

Note

The I polynomial is ignored.

Examples

um1 <- um(i = "(1 - B)(1 - B^12)", ma = "(1 - 0.8B)(1 - 0.8B^12)")
s <- spec(um1, lag.max = 13)

Standardize time series

Description

std standardizes a time series.

Usage

std(x)

Arguments

Value

The standardized time series.

Structural Time Series models

Description

stsm creates an S3 object representing a time-invariant structural time series model.

Usage

stsm(y, b, C, fSv, s2v, s2u = 1, xreg = NULL, bc = FALSE, fit = TRUE, ...)

Arguments

Details

y_t = b'x_t + u_t (observation equation), x_t = Cx_t-1 + v_t (state equation).

Value

An object of class stsm.

References

Durbin, J. and Koopman, S.J. (2012) Time Series Analysis

Examples

# Local level model
b <- 1
C <- as.matrix(1)
stsm1 <- stsm(Nile, b, C, s2v = c(lvl = 0.5), s2u = c(irr = 1))
stsm1

Sum of univariate (ARIMA) models

Description

sum_um creates a univariate (ARIMA) model from the sum of serveral univariate (arima) models.

Usage

sum_um(...)

Arguments

Value

A "um" S3 object.

Examples

um1 <- um(i = "(1 - B)", ma = "(1 - 0.8B)")
um2 <- um(i = "(1 - B12)", ma = "(1 - 0.8B^12)")
um3 <- sum_um(um1, um2)

Summarizing Transfer Function models

Description

summary method for class "tfm".

Usage

## S3 method for class 'tfm'
summary(
  object,
  y = NULL,
  method = c("exact", "cond"),
  digits = max(3L, getOption("digits") - 3L),
  envir = NULL,
  ...
)

Arguments

Value

A tfm object.

Summary of um model

Description

summary prints a summary of the estimation and diagnosis.

Usage

## S3 method for class 'um'
summary(
  object,
  z = NULL,
  method = c("exact", "cond"),
  digits = max(3L, getOption("digits") - 3L),
  envir = NULL,
  ...
)

Arguments

Value

A list with the summary of the estimation and diagonosis.

Examples

z <- AirPassengers
airl <- um(z, i = list(1, c(1,12)), ma = list(1, c(1,12)), bc = TRUE)
summary(airl)

Transfer function for input

Description

tf creates a rational transfer function for an input, V(B) = w0(1 - w_1B - ... - w_qB^q)/(1-d_1B - ... - d_pB^p)B^dX_t. Note that in this specification the constant term of the MA polynomial is factored out so that both polynomials in the numerator and denominator are normalized and can be specified with the lagpol function in the same way as the operators of univariate models.

Usage

tf(
  x = NULL,
  delay = 0,
  w0 = 0,
  ar = NULL,
  ma = NULL,
  um = NULL,
  n.back = NULL,
  par.prefix = "",
  envir = NULL
)

Arguments

Value

An object of the class "tf".

References

Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015) Time Series Analysis: Forecasting and Control. John Wiley & Sons, Hoboken.

Wei, W.W.S. (2006) Time Series Analysis Univariate and Multivariate Methods. 2nd Edition, Addison Wesley, New York, 33-59.

See Also

um.

Examples

x <- rep(0, 100)
x[50] <- 1
tfx <- tf(x, w0 = 0.8, ar = "(1 - 0.5B)(1 - 0.7B^12)")

Preestimates of a transfer function

Description

tfest provides preestimates of the transfer function between an output and an input.

Usage

tfest(
  y,
  x,
  delay = 0,
  p = 1,
  q = 2,
  um.y = NULL,
  um.x = NULL,
  n.back = NULL,
  par.prefix = "",
  envir = NULL
)

Arguments

Value

A "tf" S3 object

Transfer function models

Description

tfm creates a multiple input transfer function model.

Usage

tfm(
  output = NULL,
  xreg = NULL,
  inputs = NULL,
  noise,
  fit = TRUE,
  envir = NULL,
  new.name = TRUE,
  ...
)

Arguments

Value

An object of the class tfm.

References

Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015) Time Series Analysis: Forecasting and Control. John Wiley & Sons, Hoboken.

See Also

tf and um.

Unscramble MA polynomial

Description

Unscramble MA polynomial

Usage

theta(um)

## S3 method for class 'um'
theta(um)

Arguments

Value

A numeric vector c(1, a1, ..., ad)

Note

This function returns the member variable um$theta.

Examples

um1 <- um(ma = "(1 - 0.8B)(1 - 0.5B)")
theta(um1)

Diagnostic Plots for Time-Series Fits Description

Description

tsdiag.tfm is a wrap of the stats::tsdiag function.

Usage

## S3 method for class 'tfm'
tsdiag(object, gof.lag = 10, ...)

Arguments

See Also

stats::tsdiag.

Diagnostic Plots for Time-Series Fits Description

Description

tsdiag.um is a wrap of the stats::tsdiag function.

Usage

## S3 method for class 'um'
tsdiag(object, gof.lag = 10, ...)

Arguments

See Also

stats::tsdiag.

Value of a time series at a date

Description

tsvalue select a value from a time series by date.

Usage

tsvalue(x, date)

Arguments

Value

The value of the observation, double.

Unobserved components

Description

ucomp estimates the unobserved components of a time series (trend, seasonal, cycle, stationary and irregular) from the eventual forecast function.

Usage

## S3 method for class 'tfm'
ucomp(
  mdl,
  y = NULL,
  method = c("mixed", "forecast", "backcast"),
  envir = NULL,
  ...
)

ucomp(mdl, ...)

## S3 method for class 'um'
ucomp(
  mdl,
  z = NULL,
  method = c("mixed", "forecast", "backcast"),
  envir = NULL,
  ...
)

Arguments

Value

A matrix with the unobserved components.

Examples

Z <- AirPassengers
um1 <- um(Z, i = list(1, c(1, 12)), ma = list(1, c(1, 12)), bc = TRUE)
uc <- ucomp(um1)

Univariate (ARIMA) model

Description

um creates an S3 object representing a univariate ARIMA model, which can contain multiple AR, I and MA polynomials, as well as parameter restrictions.

Usage

um(
  z = NULL,
  ar = NULL,
  i = NULL,
  ma = NULL,
  mu = NULL,
  sig2 = 1,
  bc = FALSE,
  fit = TRUE,
  envir = parent.frame(),
  ...
)

Arguments

Value

An object of class um.

References

Box, G.E.P., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015) Time Series Analysis: Forecasting and Control. John Wiley & Sons, Hoboken.

Examples

ar1 <- um(ar = "(1 - 0.8B)")
ar2 <- um(ar = "(1 - 1.4B + 0.8B^2)")
ma1 <- um(ma = "(1 - 0.8B)")
ma2 <- um(ma = "(1 - 1.4B + 0.8B^2)")
arma11 <- um(ar = "(1 - 1.4B + 0.8B^2)", ma = "(1 - 0.8B)")

Variable selection

Description

varsel omits non-significant inputs from a transfer function model.

Usage

varsel(tfm, ...)

## S3 method for class 'tfm'
varsel(tfm, y = NULL, p.value = 0.1, envir = NULL, ...)

Arguments

Value

A tfm object or a "um" if no input is significant at that level.