R: Periodic Autoregression for a Scalar Time Series

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.
`subset` | 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 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)

[Package timsac version 1.3.6 Index]