Abstract
A stationary stochastic process that serves as a useful model for time series analysis is the autoregressive process with moving average residuals {y t } which satisfies
, t = ..., - 1, 0, 1,..., where the sequence {v t } consists of independently identically distributed (unobservable) random variables. To avoid indeterminancy β 0 = α 0 = 1. The mean of v t is independent of t and is taken to be 0 for convenience; the variance of v t is σ 2. We shall assume that the v t ’s are normally distributed, that is, that the process is Gaussian.
Research supported by the U.S. Office of Naval Research under Contract Number N00014-67-A-0112-0030. The author thanks Paul Shaman for helpful discussions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. W. Anderson: The statistical analysis of time series. Wiley, New York 1971.
T. W. Anderson: Asymptotically efficient estimation of covariance matrices with linear structure. Ann. Statistics 1 (1973), 135–141.
T. W. Anderson: Maximum likelihood estimation of parameters of autoregressive process with moving average residuals and other covariance matrices with linear structure. Ann. Statistics 3 (1975), 1283–1304.
P. Shaman: Approximations for stationary covariance matrices and their in verses with application to ARMA models. Ann. Statistics 4 (1976), 292–301.
P. Whittle: Estimation and information in stationary time series. Ark. Mat. Fys. Ast. 2 (1953), 423–434.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
About this chapter
Cite this chapter
Anderson, T.W. (1977). On Maximum Likelihood Estimation of Parameters of Autoregressive Moving Average Processes. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_4
Download citation
DOI: https://doi.org/10.1007/978-94-010-9910-3_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9912-7
Online ISBN: 978-94-010-9910-3
eBook Packages: Springer Book Archive