Journal ArticleDOI
On the inverses of some patterned matrices arising in the theory of stationary time series
R. F. Galbraith,J. I. Galbraith +1 more
TLDR
In this paper, the determinant and inverse of the covariance matrix of a set of n consecutive observations on a mixed autoregressive moving average process are given for the general autoregression process of order p (n? p), and for the first order mixed auto-regression process.Abstract:
Expressions are obtained for the determinant and inverse of the covariance matrix of a set of n consecutive observations on a mixed autoregressive moving average process. Explicit formulae for the inverse of this matrix are given for the general autoregressive process of order p (n ? p), and for the first order mixed autoregressive moving average process.read more
Citations
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Journal ArticleDOI
Long memory processes and fractional integration in econometrics
TL;DR: A survey and review of the major econometric work on long memory processes, fractional integration, and their applications in economics and finance and some of the definitions of long memory are reviewed.
Journal ArticleDOI
Maximum Likelihood Fitting of ARMA Models to Time Series With Missing Observations
TL;DR: In this paper, the exact likelihood function of a stationary autoregressive moving average (ARMA) time series based on Akaike's Markovian representation and using Kalman recursive estimation is reviewed.
Journal ArticleDOI
The likelihood function of stationary autoregressive-moving average models
Greta M. Ljung,George E. P. Box +1 more
TL;DR: In this paper, the authors examined the likelihood function of a stationary autoregressive moving average model of order (p,q) and presented a method for its evaluation, showing the computational efficiency of the method.
Journal ArticleDOI
Maximum likelihood estimation of regression models with autoregressive-moving average disturbances
Andrew Harvey,G. D. A. Phillips +1 more
TL;DR: In this paper, the regression model with autoregressive-moving average disturbances is cast in a form suitable for the application of Kalman filtering techniques, which enables the generalized least squares estimator to be calculated without evaluating and inverting the covariance matrix of the disturbances.
Journal ArticleDOI
Multiple time series analysis and the final form of econometric models
TL;DR: In this paper, the authors consider the interrelationships between the various representations of the system, and develop joint estimation and model selection procedures for the multiple time series model which arises as a multivariate representation of the individual autoregressive moving average models.
References
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Book
Time series analysis, forecasting and control
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
Journal ArticleDOI
Time Series Analysis Forecasting and Control
TL;DR: This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.