perars {timsac}R Documentation

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(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,...,nd, j=1,...,ni) is defined by

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

z(i,j) = c(j) + A(1,j,0)z(i,1) + ... + A(j-1,j,0)z(i,j-1) + A(1,j,1)z(i-1,1) + ... + A(ni,j,1)z(i-1,ni) + ... + 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 = nlog(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.
ord specification of i-th regressor (i=1,...,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 formar.
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(Airpolution)
  z <- perars(Airpolution, ni=6, lag=2, ksw=1)
  z$regcoef
  z$v

[Package timsac version 1.2.1 Index]