pear (version 1.2)

pepsi: moving average expansion of a periodic autoregression

Description

A periodic autoregression can be represented as an infinite periodic moving average process. This function calculates the coefficients in this expansion. These coefficients are needed in various time series computations such as in computing the variances of forecasts, variances of residual autocorrelations and theoretical autocovariances of a periodic autoregression. The function pepsi is used by pear to calculate the estimated standard deviations of the residual autocorrelations in a fitted periodic autoregression.

Usage

pepsi(phi, lag.max)

Arguments

phi

matrix with (i,j)-entry phi[i, j] where phi[i,j] is the autoregressive coefficient for period i at lag j. Here i=1,...,p and j=1,...,m where m is highest ar order specified.

lag.max

maximum number of lags to calculate in the moving average expansion.

Value

matrix with (i,j)-entry psi[i, j] where psi[i,j] is the autoregressive coefficient for period i at lag j. Here i=1,...,p and j=1,...,lag.max.

Side Effects

none

Details

The moving average expansion for a periodic autoregressive is defined in equation (1.4) of McLeod (1994) and the algorithm implements the recursion given in equation (1.5).

References

McLeod, A.I. (1994), "Diagnostic Checking of Periodic Autoregression" Journal of Time Series Analysis, Vol. 15, No. 2, pp.221--233.

See Also

pear

Examples

data(Fraser)
pear.out <- pear(log(Fraser), ic="bic")
pepsi(pear.out$phi,lag.max=20)