compose.mar1s {mar1s}

Compose and Decompose MAR(1)S Process

Description

compose.mar1s composes MAR(1)S process realization by given vector of log-innovations.

decompose.mar1s extracts MAR(1)S process components from time series.

Usage

compose.mar1s(object, loginnov, start.time = head(time(loginnov), 1),
              xreg.absdata = NULL, init.absdata = NULL)

decompose.mar1s(object, absdata, start.time = head(time(absdata), 1),
                init.absdata = rep(NA, NCOL(absdata)))

Arguments

object

An object of class "mar1s" specifying the model parameters.

loginnov

A univariate time series containing the log-innovations.

absdata

A univariate or multivariate time series containing the process realization.

start.time

The sampling time for the first simulation step.

xreg.absdata

A matrix-like object with row count = n.ahead, specifying the values for the external regressors. If NULL, default values are used.

init.absdata

A vector specifying the initial values of the process. If NULL, default values are used.

Details

Multiplicative AR(1) with Seasonal (MAR(1)S) process is defined as

x_t = exp(s_t + y_t)

y_{t, 1} = b_1 y_{t, 2} + \dots + b_k y_{t, k + 1} + z_t

z_t = a z_{t-1} + e_t

where

s_t is the log-seasonal component,

y_t is the AR(1) (log-stochastic) component,

e_t is the log-residuals (random component).

Value

absdata

Realization of the process (a univariate or multivariate time series object).

logdata

Logarithm of absdata (a univariate or multivariate time series object).

logstoch

Log-stochastic component (a univariate or multivariate time series object).

logresid

Random component (a univariate time series object).

Note

decompose.mar1s and fit.mar1s compute the random component in different ways: decompose.mar1s uses filter while fit.mar1s saves the residuals returned by arima. The results may be different in:

the first value:

decompose.mar1s uses specified init.absdata while arima always assumes zero initial values for the fitted process;

non-finite values:

decompose.mar1s handles non-finite values more accurately.

See Also

compose.ar1 for the AR(1) with external regressors processes, fit.mar1s for fitting MAR(1)S process to data, sim.mar1s for MAR(1)S process simulation and prediction.

Examples

data(forest.fire, package = "mar1s")
data(nesterov.index, package = "mar1s")

## Simple
mar1s <- fit.mar1s(window(forest.fire, 1969, 1989))

x <- ts(rnorm(365, sd = mar1s$logresid.sd), start = c(1989, 1))
plot(compose.mar1s(mar1s, x)$absdata)

decomp <- decompose.mar1s(mar1s, mar1s$decomposed$absdata)
delta <- abs(nan2na(mar1s$decomposed$logresid) -
             nan2na(decomp$logresid))
stopifnot(all(na.exclude(tail(delta, -1)) < 1E-6))

## External regressors
mar1s <- fit.mar1s(window(forest.fire, 1969, 1989),
                   window(nesterov.index[, "mean"], 1969, 1989))

x <- rnorm(365, sd = mar1s$logresid.sd)
xreg <- window(nesterov.index[, "mean"], 1989.001, 1990)
plot(compose.mar1s(mar1s, x, c(1989, 1), xreg)$absdata)

decomp <- decompose.mar1s(mar1s, mar1s$decomposed$absdata)
delta <- abs(mar1s$decomposed$logstoch - decomp$logstoch)
stopifnot(all(na.exclude(delta) < 1E-6))
delta <- abs(nan2na(mar1s$decomposed$logresid) -
             nan2na(decomp$logresid))
stopifnot(all(na.exclude(tail(delta, -1)) < 1E-6))