pear (version 1.2)

pepacf: periodic partial autocorrelation function

Description

The periodic partial autocorrelation function of a periodic time series is calculated and plotted if the argument plot=TRUE. When the period, p=1, this reduces to the usual partial autocorrelation function as defined in Box and Jenkins (1976) and is equivalent then to the Splus function acf(type="partial"). As discussed in Box and Jenkins (1976), McLeod (1994) and Hipel and McLeod (1994) the partial autocorrelation is a valuable tool in selecting the model order.

Usage

pepacf(z, lag.max, plot=TRUE, acf.out)

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.

lag.max

maximum lag, if missing default is 0.25*length(z)/p, where p = attr(z, "tsp")[3]

plot

if plot=TRUE, a plot of the periodic autocorrelations is produced.

acf.out

output from peacf function. If this is provided, execution will proceed faster, otherwise it is calculated from scratch.

Value

a list containing the following components: acf.out output list from peacf pacf matrix of partial autocorrelations residual.sd matrix of residual standard deviations of the fitted models of order m, m=1,2,...,lag.max phi matrix of autoregressive coefficients in the final model of order lag.max for each period aic matrix of aic values for each period and lag bic matrix of bic values for each period and lag maice vector of length p of the minimum aic models mbice vector of length p of the minimum bic models

Side Effects

a plot is produced if plot=TRUE

Details

For the detailed derivation of the algorithm see Sakai (1982). Note that our partial autocorrelation is the negative of that given in Sakai's paper.

The paper of Noakes et al. (1987) and the book of Hipel and McLeod (1994) contain examples of this type of plot.

References

Box, G.E.P. and Jenkins, G.M. (1976), "Time Series Analysis: Forecasting and Control", Holden-Day: San Franciso.

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.

Noakes, D.J., Hipel, K.W. & McLeod, A.I. (1987). Forecasting experiments with annual geophysical time series, The International Journal of Forecasting, V.4, pp.103--115.

Sakai, H. (1982), "Circular lattice filtering using Pagano's Method", IEEE Transactions, Acoust. Speech, Signal Processing, Vol. 30, pp.279--287.

See Also

peacf, peacf.plot, peplot, acf, acf.plot

Examples

data(Fraser)
pepacf(log(Fraser))