compose.ar1: Compose and Decompose AR(1) Process

Description

compose.ar1 composes AR(1) process realization by given vector(s) of innovations.

decompose.ar1 extracts AR(1) process residuals from time series.

Usage

compose.ar1(arcoef, innov, init = 0, xregcoef = 0, xreg = NULL,
            init.xreg = rep(0, length(xregcoef)))
decompose.ar1(arcoef, data, init = NA, xregcoef = 0, xreg = NULL,
              init.xreg = rep(NA, length(xregcoef)))

Arguments

arcoef

A number specifying autoregression coefficient.

innov

A univariate or multivariate time series containing the innovations.

data

A univariate or multivariate time series containing the process realization(s).

init

A number specifying the value of the process just prior to the start value in innov/data.

xregcoef

A vector specifying coefficients for the external regressors.

xreg

A matrix-like object of the same row count as innov/data, specifying the values of external regressors. The default NULL means zeroes.

init.xreg

A vector specifying the values of external regressors just prior to the start values in xreg. The default NULL means zeroes.

Value

An object of the same type and dimensions as innov/data (typically time series).

Details

Here AR(1) process with external regressors is a linear regresson with AR(1) model for the error term:

$$y_t = b_1 x_{t, 1} + \dots + b_k x_{t, k} + z_t$$

$$z_t = a z_{t-1} + e_t$$

Use xreg = NULL for the regular AR(1) process.

Examples

Run this code

# NOT RUN {
## Simple
e <- ts(c(0, 1, 0, 1, 0), freq = 12)
compose.ar1(0.1, e)
compose.ar1(0.1, e, 1)

x <- ts(c(0, 1, 0, 1, 0), freq = 12)
decompose.ar1(0.1, x)
decompose.ar1(0.1, x, 1)

## Multiseries
compose.ar1(0.1, ts(cbind(0, 1)))
compose.ar1(0.1, ts(cbind(c(0, 1, 0), c(1, 0, 1))))

decompose.ar1(0.1, ts(cbind(0, 1)))
decompose.ar1(0.1, ts(cbind(c(0, 1, 0), c(1, 0, 1))))

## External regressors
xreg1 <- rep(2, 5)
xreg2 <- matrix(rep(c(2, 1), each = 5), 5, 2)
e <- ts(c(0, 1, 0, 1, 0), freq = 12)
compose.ar1(0.1, e, xregcoef = 0.5, xreg = xreg1)
compose.ar1(0.1, e, xregcoef = 0.5, init = 0, xreg = xreg1, init.xreg = -2)
compose.ar1(0.1, e, xregcoef = c(1, -1), xreg = xreg2)

x <- ts(c(0, 1, 0, 1, 0), freq = 12)
decompose.ar1(0.1, x, xregcoef = 0.5, xreg = xreg1)
decompose.ar1(0.1, x, xregcoef = 0.5, init = 0, xreg = xreg1, init.xreg = -2)
decompose.ar1(0.1, x, xregcoef = c(1, -1), xreg = xreg2)

## Back-test
a <- 0.5
innov <- ts(rnorm(10), frequency = 12)
init <- 1
xrcoef <- seq(-0.1, 0.1, length.out = 3)
xreg <- matrix(1:30, 10, 3)
init.xreg <- 1:3
x <- compose.ar1(a, innov, init, xrcoef, xreg, init.xreg)
r <- decompose.ar1(a, x, init, xrcoef, xreg, init.xreg)
stopifnot(all.equal(innov, r))
# }