A structured state space approach to computing the likelihood of an ARIMA process and its derivatives

DOI10.1080/00949658508810810zbMath0595.62092OpenAlexW2059152853MaRDI QIDQ3727188

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/10.1080/00949658508810810

zbMATH Keywords

derivativesmissing observationsstate space approachgeneral nonstationary Gaussian ARIMA processKohn-Ansley likelihoodmodified Kalman filter algorithm

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Algorithms for approximation of functions (65D15) Numerical differentiation (65D25)

Related Items

INITIALIZING THE KALMAN FILTER FOR NONSTATIONARY TIME SERIES MODELS ⋮ Recursive estimation in econometrics ⋮ Analytic derivatives for estimation of linear dynamic models

Uses Software

• AS 154
• AS 197

Cites Work

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• Covariance matrix computation of the state variable of a stationary Gaussian process
• Algorithm AS 197: A Fast Algorithm for the Exact Likelihood of Autoregressive-Moving Average Models
• 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