perars: Periodic Autoregression for a Scalar Time Series

In timsac: Time Series Analysis and Control Package

Periodic Autoregression for a Scalar Time Series

Description

This is the program for the fitting of periodic autoregressive models by the method of least squares realized through householder transformation.

Usage

  perars(y, ni, lag = NULL, ksw = 0)

Arguments

y	a univariate time series.
ni	number of instants in one period.
lag	maximum lag of periods. Default is 2 \sqrt{\code{ni}}.
ksw	integer. '0' denotes constant vector is not included as a regressor and '1' denotes constant vector is included as the first regressor.

Details

Periodic autoregressive model (i=1, \ldots, nd, j=1, \ldots, ni) is defined by

z(i,j) = y(ni(i-1)+j),

z(i,j) = c(j) + A(1,j,0)z(i,1) + \ldots + A(j-1,j,0)z(i,j-1) + A(1,j,1)z(i-1,1) + \ldots + A(ni,j,1)z(i-1,ni) + \ldots + u(i,j),

where nd is the number of periods, ni is the number of instants in one period and u(i,j) is the Gaussian white noise. When ksw is set to '0', the constant term c(j) is excluded.

The statistics AIC is defined by AIC = n \log(det(v)) + 2k, where n is the length of data, v is the estimate of the innovation variance matrix and k is the number of parameters. The outputs are the estimates of the regression coefficients and innovation variance of the periodic AR model for each instant.

Value

mean	mean.
var	variance.
subset	specification of i-th regressor (i=1, \ldots ,ni).
regcoef	regression coefficients.
rvar	residual variances.
np	number of parameters.
aic	AIC.
v	innovation variance matrix.
arcoef	AR coefficient matrices. arcoef[i,,k] shows i-th regressand of k-th period former.
const	constant vector.
morder	order of the MAICE model.

References

M.Pagano (1978) On Periodic and Multiple Autoregressions. Ann. Statist., 6, 1310–1317.

H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.

Examples

data(Airpollution)
perars(Airpollution, ni = 6, lag = 2, ksw = 1)

timsac documentation built on Sept. 30, 2023, 5:06 p.m.