The exact likelihood function of multivariate autoregressive-moving average models
BiometrikaPublished 1 January 1979
D. F. Nicholls, Anthony Hall
Citations70
SJR quartileQ1
SJR score3.60
SNIP2.67
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
By making use of the properties of tensor products, this paper describes the derivation of an expression for the exact likelihood function of a stationary process generated by a vector autoregressive-moving average model using concentrated maximum likelihood techniques. Furthermore, in the process of deriving the likelihood function, a closed form expression for the covariance function of the process in terms of the coefficients of the model is derived.
Keywords
Decision SciencesEngineering
BiometrikaMaximum likelihood identification of Gaussian autoregressive moving average models
1,392 Citations1973HTROTUGU AKAIKE
It is shown that the procedure described by Hannan (1969) for the estimation of the parameters of one-dimensional autoregressive moving average processes is equivalent to a three-stage realization of one step of the NewtonRaphson procedure for the numerical maximization of the likelihood function, using the gradient and the approximate Hessian.
Journal of the American Statistical AssociationSome Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix Products
278 Citations1969Heinz Neudecker
Advances in Applied ProbabilityVector linear time series models
274 Citations1976William T. M. Dunsmuir, E. J. Hannan
BiometrikaAn algorithm for the exact likelihood of a mixed autoregressive-moving average process
270 Citations1979Craig F. Ansley
The likelihood function for an autoregressive-moving average process is obtained by transforming the process to obtain a band covariance matrix whose Cholesky decomposition can be readily computed.
BiometrikaThe exact likelihood function for a mixed autoregressive-moving average process
152 Citations1974Paul Newbold
BiometrikaThe estimation of mixed moving average autoregressive systems
114 Citations1969E. J. Hannan
International Economic ReviewThe Estimation and Use of Models with Moving Average Disturbance Terms: A Survey
90 Citations1975D. F. Nicholls, A. R. Pagan +1 more
IEEE Transactions on Information TheoryMaximum likelihood estimation of parameters in multivariate Gaussian stochastic processes (Corresp.)
65 Citations1974Peter E. Caines, J. Rissanen
A proof of the strong consistency of the maximum likelihood estimate of the parameters of Gaussian random processes possessing linear autoregressive moving average or state space representations is outlined.
BiometrikaComputation of the exact likelihood function of multivariate moving average models
52 Citations1978Mihir Phadke, Gershon Kedem
BiometrikaAnalysis of autoregressive-moving average models: Estimation and prediction
46 Citations1977MUKETAR M. ALI
Journal of Statistical Computation and SimulationComputation of the exact likelihood function of an arima process
39 Citations1977Warren T. Dent
BiometrikaThe efficient estimation of vector linear time series models
38 Citations1976D. F. Nicholls
The Review of Economic StudiesExact Maximum Likelihood Estimation of Regression Models with Finite Order Moving Average Errors
21 Citations1976A. R. Pagan, D. F. Nicholls
BiometrikaA comparison of estimation methods for vector linear time series models
13 Citations1977D. F. Nicholls
