| Type: | Package |
| Title: | Transfer Function and ARIMA Models |
| Version: | 0.3.2 |
| Date: | 2022-05-20 |
| Description: | Building customized transfer function and ARIMA models with multiple operators and parameter restrictions. Functions for model identification, model estimation (exact or conditional maximum likelihood), model diagnostic checking, automatic outlier detection, calendar effects, forecasting and seasonal adjustment. See Bell and Hillmer (1983) <doi:10.1080/01621459.1983.10478005>, Box, Jenkins, Reinsel and Ljung <ISBN:978-1-118-67502-1>, Box, Pierce and Newbold (1987) <doi:10.1080/01621459.1987.10478430>, Box and Tiao (1975) <doi:10.1080/01621459.1975.10480264>, Chen and Liu (1993) <doi:10.1080/01621459.1993.10594321>. |
| Author: | Jose L. Gallego [aut, cre] |
| Maintainer: | Jose L. Gallego <jose.gallego@unican.es> |
| URL: | https://github.com/gallegoj/tfarima |
| License: | GPL-2 |
| Imports: | Rcpp (≥ 1.0.0), stats, numDeriv, zoo |
| LinkingTo: | Rcpp, RcppArmadillo |
| Suggests: | knitr, rmarkdown |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.2 |
| Depends: | R (≥ 2.10) |
| VignetteBuilder: | knitr |
| NeedsCompilation: | yes |
| Packaged: | 2022-05-20 10:19:15 UTC; jose |
| Repository: | CRAN |
| Date/Publication: | 2022-05-20 10:50:02 UTC |
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
x |
an object of class |
form |
a character indicated the set of calendar variables: td, td7, td6, wd. |
ref |
a non-negative integer indicating the reference day. |
lom |
logical. If TRUE length of the month effect is also estimated. |
lpyear |
logical. If TRUE a leap year effect is also estimated. |
easter |
logical. If TRUE an additional deterministic variable is generated to capture Easter effects. |
len |
duration of the Easter, integer. |
easter.mon |
logical. It is TRUE if Holy Monday is a public holiday. |
n.ahead |
number of additional observations to extend the sample period. |
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
Y |
an object of class |
date |
the date of the event, c(year, month). |
type |
a character indicating the type of intervention variables: (P) pulse, (S) step, (R). |
n.ahead |
number of additional observations to extend the sample period. |
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
x |
an |
extend |
logical. If TRUE, the transformed series is extended with NA's to have the same length as the origianl series. |
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
pol |
a numeric vector. |
p |
integer power. |
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
arima |
an object of class |
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
um |
an object of class |
... |
additional arguments. |
lag.max |
maximum lag for autocovariances. |
par |
logical. If TRUE partial autocorrelations are computed. |
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
mdl |
an object of class |
... |
additional arguments. |
lag.max |
maximum lag for autocovariances. |
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
y |
an object of class |
bc |
logical. If TRUE logs are taken. |
seas |
character, type of seasonality (Harvey-Durbin (hd), Harvey-Todd (ht), Harrison-Steven (ht)) |
s2v |
variances of the error vector v_t. |
s2u |
variance of the error u_t. |
xreg |
matrix of regressors. |
fSv |
function to create the covariance matrix of v_t. |
... |
other 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
mdl |
|
y |
a time series. |
form |
representation for calendar effects: (1) |
ref |
a integer indicating the the reference day. By default, ref = 0. |
lom, lpyear |
a logical value indicating whether or not to include the lom/lead year indicator. |
easter |
logical. If |
len |
the length of the Easter, integer. |
easter.mon |
logical. TRUE indicates that Easter Monday is a public holiday. |
n.ahead |
a positive integer to extend the sample period of the
deterministic variables with |
p.value |
estimates with a p-value greater than p.value are omitted. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
other 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
tfm |
a |
lag.max |
number of lags. |
method |
Exact/conditional residuals. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional 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
object |
a |
... |
other 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
object |
a |
... |
other 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
mdl |
an object of class |
y |
an object of class |
method |
exact or conditional residuals. |
lag.max |
number of lags for ACF/PACF. |
lags.at |
the lags of the ACF/PACF at which tick-marks are to be drawn. |
freq.at |
the frequencies of the (cum) periodogram at at which tick-marks are to be drawn. |
std |
logical. If TRUE standardized residuals are shown. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional arguments. |
z |
optional, an object of class |
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
um |
an object of class |
... |
additional arguments. |
lag.max |
number of lags for ACF/PACF. |
n.freq |
number of frequencies for the spectrum. |
log.spec |
logical. If TRUE log spectrum is computed. |
graphs |
vector of graphs. |
byrow |
orientation of the graphs. |
eq |
logical. If TRUE the model equation is used as title. |
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
um |
an object of class |
... |
other arguments. |
z |
a time series. |
len |
a positive integer specifying the duration of the Easter. |
easter.mon |
logical. If TRUE Easter Monday is also taken into account. |
n.ahead |
a positive integer to extend the sample period of the
Easter regression variable with |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
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
mdl |
an object of class |
method |
argument of the |
show.iter |
logical value to show or hide the estimates at the different iterations. |
... |
other 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
mdl |
|
y |
a |
method |
Exact/conditional maximum likelihood. |
optim.method |
the |
show.iter |
logical value to show or hide the estimates at the different iterations. |
fit.noise |
logical. If TRUE parameters of the noise model are fixed. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional arguments. |
z |
a time series. |
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
mdl |
an object of class |
... |
other arguments. |
g |
a vector of theoretical autocovariances (gamma[k], k= 0, ..., K). |
method |
optimation method. |
show.iter |
logical. If TRUE, estimates at each iteration are printed. |
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
Y |
Univariate or multivariate time series. |
transf |
Data transformations, list(bc = F, d = 0, D = 0, S = F), where bc is the Box-Cox logarithmic transformation, d and D are the number of nonseasonal and seasonal differences, and S is the annual sum operator. |
order.polreg |
an integer indicating the order of a polynomial trend. |
lag.max |
number of autocorrelations. |
lags.at |
the lags of the ACF/PACF at which tick-marks are to be drawn. |
freq.at |
the frequencies of the (cum) periodogram at at which tick-marks are to be drawn. |
wn.bands |
logical. If TRUE confidence intervals for sample autocorrelations are computed assuming a white noise series. |
graphs |
graphs to be shown: plot, hist, acf, pacf, pgram, cpgram (cummulative periodogram), rm (range-median). |
set.layout |
logical. If TRUE the layout is set by the function, otherwise it is set by the user. |
byrow |
logical. If TRUE the layout is filled by rows, otherwise it is filled by columns. |
main |
title of the graph. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional 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
mdl |
|
y |
a "ts" object, optional. |
type |
the type intervention (pulse, step, ramp) or the type of outlier (AO, LS, TC, IO). |
time |
the date of the intervention, in format c(year, season). |
n.ahead |
a positive integer to extend the sample period of the
intervention variable with |
envir |
the environment in which to look for the time series z when it is passed as a character string. |
... |
additional 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
lp |
an object of class |
... |
additional arguments. |
lag.max |
largest order of the inverse lag polynomial. |
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
param |
a vector/list of named parameters. |
s |
the seasonal period, integer. |
p |
the power of lag polynomial, integer. |
lags |
a vector of lags for sparse polynomials. |
coef |
a vector of math expressions. |
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
object |
an object of class |
z |
an object of class |
method |
exact or conditional. |
... |
additional 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
mdl |
an object of class |
... |
additional arguments. |
ar |
list of stationary AR lag polynomials. |
i |
list of nonstationary AR (I) polynomials. |
ma |
list of MA polynomials. |
mu |
mean of the stationary time series. |
sig2 |
variance of the error. |
bc |
logical. If TRUE logs are taken. |
fit |
logical. If TRUE, model is fitted. |
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
um |
an object of class |
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
tfm |
an object of the class |
... |
additional arguments. |
y |
output of the TF model if it is different to that of the
|
diff |
logical. If TRUE, the noise is differenced with the "i" operator of the univariate model of the noise. |
exp |
logical. If TRUE, the antilog transformation is applied. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
Value
A "ts" object.
Outlier dates
Description
outlierDates shows the indeces and dates of outliers.
Usage
outlierDates(x, c = 3)
Arguments
x |
an |
c |
critical value to determine whether or not an observation is an outlier. |
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
mdl |
|
y |
an object of class |
types |
a vector with the initials of the outliers to be detected, c("AO", "LS", "TC", "IO"). |
dates |
a list of dates c(year, season). If |
c |
a positive constant to compare the z-ratio of the effect of an
observation and decide whether or not it is an outlier. This argument is
only used when |
calendar |
logical; if true, calendar effects are also estimated. |
easter |
logical; if true, Easter effect is also estimated. |
resid |
type of residuals (exact or conditional) used to identify outliers. |
n.ahead |
a positive integer to extend the sample period of the
intervention variables with |
p.value |
estimates with a p-value greater than p.value are omitted. |
tc.fix |
a logical value indicating if the AR coefficient in the transfer function of the TC is estimated or fix. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
other 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
tf |
an object of the S3 class "tf". |
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
x |
input, a 'ts' object or a numeric vector. |
y |
output, a 'ts' object or a numeric vector. |
um.x |
univariate model for input. |
um.y |
univariate model for output. |
lag.max |
number of lags, integer. |
plot |
logical value to indicate if the ccf graph must be graphed or computed. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
main |
title of the graph. |
nu.weights |
logical. If TRUE the coefficients of the IRF are computed instead of the cross-correlations. |
... |
additional 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
um |
an object of class |
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
um |
an object of class |
... |
additional arguments. |
lag.max |
largest AR(Inf) coefficient required. |
var.pi |
logical. If TRUE (FALSE), the I polynomials is considered (ignored). |
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
object |
an object of class |
newdata |
new data for the predictors for the forecast period. This is
a matrix if there is more than one predictor. The number of columns is
equal to the number of predictors, the number of rows equal to
|
y |
an object of class |
ori |
the origin of prediction. By default, it is the last observation. |
n.ahead |
number of steps ahead. |
level |
confidence level. |
i |
transformation of the series |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional 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
object |
an object of class |
z |
an object of class |
ori |
the origin of prediction. By default, it is the last observation. |
n.ahead |
number of steps ahead. |
level |
confidence level. |
i |
transformation of the series |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional 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
pol |
numeric vectors with the coefficients of a normalized polynomial. |
digits |
number of decimals. |
Print a list of lagpol objects
Description
Print a list of lagpol objects
Usage
printLagpolList(llp, digits = 2)
Arguments
llp |
a list of |
digits |
number of decimals. |
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
um |
an object of class |
... |
additional arguments. |
lag.max |
Largest MA(Inf) coefficient required. |
var.psi |
logical. If TRUE the I polynomials is also inverted. If FALSE it is ignored. |
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
object |
a |
y |
output of the TF model (if it is different to that of the "tfm" object). |
method |
a character string specifying the method to compute the residuals, exact or conditional. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional 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
object |
an object of class |
z |
an object of class |
method |
exact/conditional residuals. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional 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
mdl |
an object of class |
... |
other 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
x |
an object of class |
... |
additional arguments. |
opr |
character that indicates which operators are selected. |
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
x |
an object of class |
table |
logical. If TRUE, it returns a five columns table showing the real and imaginary parts, the modulus, the frequency and the period of each root. |
... |
additional 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
Y |
an object of class |
ref |
the reference season, positive integer |
constant |
logical indicator to include a column of ones. |
n.ahead |
number of additional observations to extend the sample period. |
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
mdl |
|
... |
additional arguments. |
z |
an object of class |
method |
forward/backward forecasts or a mixture of the two. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
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
mdl |
a |
xreg |
a matrix of inputs. |
inputs |
a list of tf objects. |
y |
an optional ts object. |
envir |
an environment. |
... |
other 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
mdl |
an object of class |
... |
other arguments. |
fSv |
optional function to create the covariance matrix. |
par |
vector of parameters for function fSv. |
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
mdl |
an object of the class |
... |
additional arguments. |
y |
output of the TF model if it is different to that of the
|
diff |
logical. If TRUE, the noise is differenced with the "i" operator of the univariate model of the noise. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
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
mdl |
an object of class |
n |
number of observations. |
y0 |
initial conditions for the nonstationary series. |
seed |
an integer. |
... |
other arguments. |
z0 |
initial conditions for the nonstationary series. |
n0 |
remove the n0 first observation, integer. |
a |
vector of innovations, optional. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
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
Y |
an object of class |
n.ahead |
number of additional observations to extend the sample period. |
constant |
logical indicator to include a column of ones. |
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
um |
an object of class |
... |
additional parameters. |
n.freq |
number of frequencies. |
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
x |
a |
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
y |
an object of class |
b |
vector of constants. |
C |
matrix of constants. |
fSv |
function to create the covariance matrix of v_t. |
s2v |
variances of the vector error v_t in the state equation. |
s2u |
variance of the error u_t in the observation equation. |
xreg |
matrix of regressors. |
bc |
logical. If TRUE logs are taken. |
fit |
logical. If TRUE, model is fitted. |
... |
other 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
... |
List of "um" S3 objects. |
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
object |
a |
y |
a "ts" object. |
method |
exact or conditional maximum likelihood. |
digits |
number of significant digits to use when printing. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional 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
object |
an object of class |
z |
an object of class |
method |
exact/conditional maximum likelihood. |
digits |
number of significant digits to use when printing. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional 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
x |
input, a ts object or a numeric vector. |
delay |
integer. |
w0 |
constant term of the polynomial V(B), double. |
ar |
list of stationary AR polynomials. |
ma |
list of MA polynomials. |
um |
univariate model for stochastic input. |
n.back |
number of backcasts to extend the input. |
par.prefix |
prefix name for parameters. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
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
y |
output, a ts object or a numeric vector. |
x |
input, a ts object or a numeric vector. |
delay |
integer. |
p |
order of the AR polynomial, integer |
q |
order of the MA polynomial, integer. |
um.y |
univariate model for output, um object or NULL. |
um.x |
univariate model for input, um object or NULL. |
n.back |
number of backcasts. |
par.prefix |
prefix name for parameters. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
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
output |
a ts object or a numeric vector. |
xreg |
a matrix of regressors. |
inputs |
a list of tf objects. |
noise |
a um object for the noise. |
fit |
logical. If TRUE, model is fitted. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
new.name |
logical. Argument used internally: if TRUE a new name is assigned to the output, otherwise it keeps its name saved in noise$z. |
... |
additional 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
Unscramble MA polynomial
Description
Unscramble MA polynomial
Usage
theta(um)
## S3 method for class 'um'
theta(um)
Arguments
um |
an object of class |
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
object |
a fitted |
gof.lag |
the maximum number of lags for a Portmanteau goodness-of-fit test |
... |
additional 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
object |
a fitted |
gof.lag |
the maximum number of lags for a Portmanteau goodness-of-fit test |
... |
additional 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
x |
an |
date |
the time of the specific observation, c(year, month/quarter). |
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
mdl |
|
y |
an object of class |
method |
forward/backward forecasts or a mixture of the two. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
... |
additional arguments. |
z |
an object of class |
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
z |
an object of class |
ar |
list of stationary AR lag polynomials. |
i |
list of nonstationary AR (I) polynomials. |
ma |
list of MA polynomials. |
mu |
mean of the stationary time series. |
sig2 |
variance of the error. |
bc |
logical. If TRUE logs are taken. |
fit |
logical. If TRUE, model is fitted. |
envir |
the environment in which to look for the time series z when it is passed as a character string. |
... |
additional 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
tfm |
a |
... |
other arguments. |
y |
a "ts" object. |
p.value |
probability value to decide whether or not to omit an input. |
envir |
environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used. |
Value
A tfm object or a "um" if no input is significant at that level.