timsac (version 1.3.0)

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)

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.

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.

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(Airpolution)
  perars(Airpolution, ni=6, lag=2, ksw=1)