Fisher Information Matrix ARMA and Fractional ARMA
Theoretical Autocovariance Function
Covariance Matrix of Residual Autocorrelations

 These pages are still under development.    09/27/04


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:

  1. McLeod, A.I. (1999), Necessary and sufficient condition for nonsingular Fisher information matrix in ARMA and fractional ARMA models.  The Americian Statistician.
  2. McLeod, A.I. (1993), A note on ARMA model parameter redundancy, The Journal of Time Series Analysis 14, 207-208. 
  3. Li, W.K. & McLeod, A.I. (1986), Fractional time series modelling, Biometrika 73, 217--221. 
  4. McLeod, A.I. (1984), Duality and other properties of multiplicative autoregressive-moving average models, Biometrika 71, 207-211. 
  5. 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. 
  6. McLeod, A.I. (1975), Derivation of the theoretical autocorrelation function of autoregressive moving-average timeseries, Applied Statistics 24, 255-256. (Errata, 26, 194). 


A 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.
bulletSplus MS Windows
A zipped Windows S-Plus 4.5 version is available, To install it, go the S-Plus library directory (default location is /"Program files"/splus45/library) and type the command:
unzip    You may wish to download: unzip.exe
bulletSplus 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
bulletFortran 77 Source Code
I 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.