Theoretical Autocovariance Function

Covariance Matrix of Residual Autocorrelations

I provide software packages in *Mathematica*, Splus and Fortran
for computing the theoretical autocovariance function, large sample Fisher information
matrix and the covariance matrix of the residual autocorrelations in ARMA and fractional
ARMA models. This software implements the methods given in the following articles:

- McLeod, A.I. (1999), Necessary and sufficient condition for nonsingular
Fisher information matrix in ARMA and fractional ARMA models.
*The Americian Statistician.* - McLeod, A.I. (1993), A note on ARMA model parameter redundancy,
*The Journal of Time Series Analysis***14**, 207-208. - Li, W.K. & McLeod, A.I. (1986), Fractional time series modelling,
*Biometrika***73**, 217--221. - McLeod, A.I. (1984), Duality and other properties of multiplicative
autoregressive-moving average models,
*Biometrika***71**, 207-211. - McLeod, A.I. (1978), On the distribution and applications of residual
autocorrelations in Box-Jenkins modelling,
*Journal of the Royal Statistical Society***B 40**, 296-302. - McLeod, A.I. (1975), Derivation of the theoretical autocorrelation
function of autoregressive moving-average timeseries,
*Applied Statistics***24**, 255-256. (Errata, 26, 194).

MathematicaA Mathematica package, AuxARMA.m, for computing symbolic autocovariance,
information matrix, model redundancy tests as well as visualizations for the
autocorrelation function and spectral density. There is an accompaning Mathematica
notebook, AuxARMA.nb which illustrates the functions in AuxARMA.m. | |

Splus MS Windows A zipped Windows S-Plus 4.5 version is available, iarma.zip. To install it, go the S-Plus library directory (default location is /"Program files"/splus45/library) and type the command: unzip iarma.zip You may wish to download: unzip.exe | |

Splus Unix Tar file, iarma.tar. To recover enter the command: tar -xvf iarma.tar Then input the file iarma.s to Splus with the source("iarma.s") and move the *.h files to the directory .Data/.Help and remove the extension .h from each file. A Korn shell script to rename the files, rename.h. To execute, simply copy to the .Help directory where all the *.h files are and then enter the command: sh rename.h | |

Fortran 77 Source CodeI provide the source code along with a driver program and Win95 executable to
compute the theoretical autocovariance function, Fisher Information matrix and the
standard deviations of the residual autocorrelations in arma, multiplicative seasonal arma
and fractional arma models. |