Computation of Theoretical Autocovariance Matrices of Multivariate Autoregressive Moving Average Time Series
- 1 September 1990
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 52 (1) , 151-155
- https://doi.org/10.1111/j.2517-6161.1990.tb01778.x
Abstract
SUMMARY: Matrix expressions relating the theoretical autocovariances of autoregressive moving average (ARMA) processes to their parameters are derived and used to design an efficient procedure for computing autocovariance sequences of multivariate ARMA processes. The method proposed is more efficient than others suggested in the literature and, in particular, reduces the computational burden associated with exact maximum likelihood estimation of ARMA models. The closed form expressions facilitate the implementation of algorithms for computing multivariate autocovariances.This publication has 12 references indexed in Scilit:
- Algorithm AS 232: Computation of Population and Sample Correlation and Partial Correlation Matrices in MARMA(P, Q) Time SeriesJournal of the Royal Statistical Society Series C: Applied Statistics, 1988
- Non-recursive methods for computing the coefficients of the autoregressive and the moving-average representation of mixed ARMA processesEconomics Letters, 1987
- A note on obtaining the theoretical autocovariances of an ARMA processJournal of Statistical Computation and Simulation, 1982
- Computation of the theoretical autocovariance function for a vector arma processJournal of Statistical Computation and Simulation, 1980
- Finite sample properties of estimators for autoregressive moving average modelsJournal of Econometrics, 1980
- Algorithm AS 154: An Algorithm for Exact Maximum Likelihood Estimation of Autoregressive-Moving Average Models by Means of Kalman FilteringJournal of the Royal Statistical Society Series C: Applied Statistics, 1980
- The exact likelihood function of multivariate autoregressive-moving average modelsBiometrika, 1979
- Derivation of the Theoretical Autocovariance Function of Autoregressive Moving Average Time SeriesJournal of the Royal Statistical Society Series C: Applied Statistics, 1975
- Block Toeplitz Matrix InversionSIAM Journal on Applied Mathematics, 1973
- Multiple Time SeriesWiley Series in Probability and Statistics, 1970