pear (version 1.2)

peacf: Periodic Autocorrelation Function

Description

The periodic autocorrelation for a time series with period p may be defined as for period (m=1,...,p) and lag, l=1,2,... by r(m, l) = c(m, l)/sqrt(c(m, 0)*c(m-l, 0)) where c(m, l) is the periodic autocovariance defined by c(m, l) = sum(z[t] * z[t-l]) where the sum is over all data in period m. When p=1, peacf produces output which is equivalent to that produced by Splus function acf.

Usage

peacf(z, lag.max, plot=TRUE)

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.

Value

a list is returned with the following components: means periodic means standard.deviations periodic standard deviations acf matrix of periodic autocorrelations benchmark.sd 1/sqrt(nyrs), nyrs=ceiling(length(z)/p) sub.lengths number of observations in each period period p = attr(z, "tsp")[3] title title = attr(z, "title") periodicity.test list: test for periodic correlation at lag 1 The components of this list are: Q1 = scalar value, the test statistic Q1.sl = signifiance level (upper tail) portmanteau.test list: portmanteau test at various lags The components of this list are: QM = matrix of portmanteau statistics for each period and lag QM.df = corresponding df of QM

Side Effects

a plot may be produced if plot=TRUE

Details

The use of the periodic autocorrelation and its plot are discussed in McLeod (1994) and a portmanteau model adequacy test is developed therein. The periodicity test is discussed in McLeod (1993). For more details, see the references below.

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. (1993), "Parsimony, Model Adequacy and Periodic Correlation in Time Series Forecasting", International Statistical Review, Vol. 61, No. 3, pp.387--393. McLeod, A.I. (1994), "Diagnostic Checking of Periodic Autoregression" Journal of Time Series Analysis, Vol. 15, No. 2, pp.221--233.

See Also

peacf.plot, pepacf, peplot, peboxplot, pear, acf, acf.plot

Examples

data(Fraser)
peacf(log(Fraser))