timsac (version 1.3.8)

perars: 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)

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.

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.

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)