Computing the likelihood and its dierivatives for a gaussian ARMA model

DOI10.1080/00949658508810849zbMath0605.62096OpenAlexW2084289000MaRDI QIDQ3742545

Robert Kohn, Craig F. Ansley

Publication date: 1985

Published in: Journal of Statistical Computation and Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00949658508810849

zbMATH Keywords

likelihoodalgorithmderivativescovariancesautoregressive moving average processseasonal modelsGaussian ARMAlag polynomials

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Algorithms for approximation of functions (65D15) Probabilistic methods, stochastic differential equations (65C99)

Related Items (11)

Fast optimization of the exact likelihood of AR and ARMA processes ⋮ Computation of the Fisher information matrix for time series models ⋮ ALGORITHMS FOR ESTIMATION OF POSSIBLY NONSTATIONARY VECTOR TIME SERIES ⋮ FISHER'S INFORMATION MATRIX FOR SEASONAL AUTOREGRESSIVE-MOVING AVERAGE MODELS ⋮ EXACT MAXIMUM LIKELIHOOD ESTIMATION IN AUTOREGRESSIVE PROCESSES ⋮ Computing the Exact Fisher Information Matrix of Periodic State-Space Models ⋮ Exact maximum likelihood estimation of structured or unit root multivariate time series models ⋮ Diagnosing seasonal shifts in time series using state space models ⋮ Modeling Covariance Parameters for Purely Autoregressive Correlated Longitudinal Data ⋮ Computation of the exact information matrix of Gaussian dynamic regression time series models ⋮ Analytic derivatives for estimation of linear dynamic models

Cites Work

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• Covariance matrix computation of the state variable of a stationary Gaussian process
• Symmetric decmposition of positive definite band matrices
• Some efficient computational procedures for high order ARMA models
• Algorithm AS 197: A Fast Algorithm for the Exact Likelihood of Autoregressive-Moving Average Models
• A note on Kalman filtering for the seasonal moving average model
• Algorithm AS 154: An Algorithm for Exact Maximum Likelihood Estimation of Autoregressive-Moving Average Models by Means of Kalman Filtering
• An algorithm for the exact likelihood of a mixed autoregressive-moving average process
• Some new algorithms for recursive estimation in constant, linear, discrete-time systems
• Maximum likelihood estimation of parameters in multivariate Gaussian stochastic processes (Corresp.)
• Evaluation of likelihood functions for Gaussian signals

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