FitARMA (version 1.6.1)

TacvfARMA: Theoretical Autocovariance Function of ARMA

Description

The theoretical autocovariance function of an ARMA(p,q) with unit variance is computed. This algorithm has many applications. In this package it is used for the computation of the information matrix, in simulating p initial starting values for AR simulations and in the computation of the exact mle for the mean.

Usage

TacvfARMA(phi = numeric(0), theta = numeric(0), lag.max = 20)

Arguments

phi

AR coefficients

theta

MA coefficients

lag.max

computes autocovariances lags 0,1,...,lag.max

Value

vector of length lag.max+1 containing the autocovariances is returned

Details

The algorithm given by McLeod (1975) is used.

The built-in R function ARMAacf could also be used but it is quite complicated and apart from the source code, the precise algorithm used is not described. The only reference given for ARMAacf is the Brockwell and Davis (1991) but this text does not give any detailed exact algorithm for the general case.

Another advantage of TacvfARMA over ARMAacf is that it will be easier for to translate and implement this algorithm in other computing environments such as MatLab etc.

References

McLeod, A.I. (1975), Derivation of the theoretical autocorrelation function of autoregressive moving-average time series, Applied Statistics 24, 255-256.

See Also

ARMAacf, InformationMatrixARMA

Examples

# NOT RUN {
#calculate and plot the autocorrelations from an ARMA(1,1) model
# with parameters phi=0.9 and theta=0.5
 g<-TacvfARMA(0.9,0.5,20)
 AcfPlot(g/g[1], LagZeroQ=FALSE)
# }