pear (version 1.2)

pear: fit a periodic autoregression model

Description

Periodic time series models of any order, say m[j], for the j-th period, j=1,...,p can be fit to a periodic time series of period p. A generalization of the Yule-Walker method is used so that when p=1 the results from this function will be equivalent to the Splus function ar.yw(). If desired the aic or bic criterion can be used to select the model orders. Otherwise the user can select based on the partial autocorrelation function as suggested in Box and Jenkins (1976) and McLeod (1994).

Usage

pear(z, m, ic="none")

Arguments

z

a univariate time series object. Note that the period of z is given by attr(z, "tsp")[3]. Additional information about the time series can be provided in a title string by setting attr(z, "title") to the desired string. This title will then be displayed on the plot. Abbreviations for the periods may be provided in attr(z, "abb"). For example, to use the standard monthly abbreviations: attr(z, "abb")<-month.abb. These abbreviations will be used to aid one in interpreting the output.

m

If ic="none" then m is a required argument. In this case m specifies the order of the periodic autoregression to be fitted. Typically m is specified as a vector of length p where p is the period and m[k], k=1,...,p indicates the order for the k-th period. For convenience, if all periods are the same order then m can just be that scalar value. When ic="aic" or ic="bic" then the argument m is ignored.

ic

The default ic="none" means the model orders are supplied. Otherwise if ic="aic" or ic="bic" the automatic criteria aic or bic are used.

Value

a list with the following named components: model.orders vector of length p, indicating the fitted ar order for each period k, k=1,...,p phi matrix of dimension p by m where m = max(model.orders). The (i,j) entry is phi[i,j] which is the autoregression coefficient for period i and lag j. se.phi matrix of standard deviations for the estimated phi's. For those phi's set to 0, the corresponding se.phi's are also set to 0. resvar vector of length p residuals time series object of length(z) portmanteau.test list: portmanteau test at various lags The named components of this list are: QM = matrix of portmanteau statistics for each period and lag QM.df = corresponding df of QM QM.sl = corresponding sl of QM residual.acf residual autocorrelation matrix residual.acf.sd estimated standard errors of the residual autocorrelations cov list with p components: cov[[i]] is the estimated covariance matrix for the parameters of period i

Side Effects

none

Details

Let z[t] be a period time series with period p and let m[j] denote the order of the autoregressive model for the j-th period, j=1,...,p. The parameters of this model can be estimated using the Yule-Walker type equations given in McLeod eq (3.1) and (3.2). The covariance matrix of the autoregressive parameters is obtained by replacing the theoretical autocovariances in eq (3.3, note addendum correction) with their sample values.

References

Hipel, K.W. and McLeod, A.I. (1994) "Time Series Modelling of Water Resources and Environmental Systems" Elsevier, Amsterdam ISBN 0-444-89270-2. (1013 pages).

McLeod, A.I. (1994), "Diagnostic Checking of Periodic Autoregression" Journal of Time Series Analysis, Vol. 15, No. 2, pp.221--233.

McLeod, A.I. (1995), Errata (see file errata.tex included with these files)

See Also

peacf, pepacf, ar.yw

Examples

data(Fraser)
pear(log(Fraser), ic="bic")