# TacvfAR: Theoretical Autocovariance Function of AR In FitAR: Subset AR Model Fitting

## Description

The theoretical autocovariance function of an AR(p) 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

 `1` ```TacvfAR(phi, lag.max = 20) ```

## Arguments

 `phi` vector of AR coefficients `lag.max` computes autocovariances lags 0,1,...,maxlag

## 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 TacvfAR over ARMAacf is that it will be easier for to translate and implement this algorithm in other computing environments such as MatLab etc. since the code is entirely written in R.

## Value

Vector of length = (lag.max+1) containing the autocovariances at lags 0,...,lag.max is returned.

A.I. McLeod

## References

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

`ARMAacf`, `InformationMatrixAR`, `GetARMeanMLE`, `SimulateGaussianAR`
 ```1 2 3 4``` ```#calculate and plot the autocorrelations from an AR(2) model # with parameter vector c(1.8,-0.9). g<-TacvfAR(c(1.8,-0.9),20) AcfPlot(g/g[1], LagZeroQ=FALSE) ```