Identification of Echelon Canonical Forms for Vector Linear Processes Using Least Squares
The Annals of StatisticsPublished 1 March 1992Open access
D. S. Poskitt
Citations47
SJR quartileQ1
SJR score4.77
SNIP3.13
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
In this paper a method of identifying stationary and invertible vector autoregressive moving-average time series is proposed. The models are presumed to be represented in (reversed) echelon canonical form. Consideration is given to both parameter estimation and the determination of structural indices, the evaluations being based on the use of closed form least squares calculations. Consistency of the technique is shown and the operational characteristics of the procedure when employed as a means of approximating more general processes is discussed.
Keywords
Engineering
IEEE Transactions on Automatic ControlA new look at the statistical model identification
50,732 Citations1974Hirotugu Akaike
Linear Regression Analysis
2,763 Citations2013Seber, George A. F. 1938-, Lee, Alan J. 1946-
TechnometricsThe Statistical Theory of Linear Systems
764 Citations1990Jonathan D. Cryer, E. J. Hannan +1 more
The Annals of StatisticsAsymptotically Efficient Selection of the Order of the Model for Estimating Parameters of a Linear Process
556 Citations1980Ritei Shibata
Proceedings of the IEEELattice filters for adaptive processing
518 Citations1982B. Friedlander
This paper presents a tutorial review of lattice structures and their use for adaptive prediction of time series, and it is shown that many of the currently used lattice methods are actually approximations to the stationary least squares solution.
Journal of the American Statistical AssociationThe Multivariate Portmanteau Statistic
486 Citations1980J. R. M. Hosking
BiometrikaA canonical analysis of multiple time series
379 Citations1977George E. P. Box, George C. Tiao
Journal of the Royal Statistical Society Series B (Statistical Methodology)Model Specification in Multivariate Time Series
360 Citations1989George C. Tiao, Ruey S. Tsay
The concept of scalar component models within the vector ARMA framework is introduced to reveal possibly hidden simplifying structures of the process, to achieve parsimony in parameterization and to identify the exchangeable models.
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
Advances in Applied ProbabilityMultivariate linear time series models
172 Citations1984E. J. Hannan, L. Kavalieris
This paper discusses the asymptotic properties of the algorithm that depend on uniform rates of convergence being established for covariances up to some lag increasing indefinitely with the length of record, T.
The Annals of StatisticsAutocorrelation, Autoregression and Autoregressive Approximation
142 Citations1982Hongzhi An, Zhaoguo Chen +1 more
Journal of Time Series AnalysisREGRESSION, AUTOREGRESSION MODELS
119 Citations1986E. J. Hannan, L. Kavalieris
The Annals of StatisticsUnit Canonical Correlations between Future and Past
57 Citations1988E. J. Hannan, D. S. Poskitt
The Annals of StatisticsDiagnostic Tests for Multiple Time Series Models
40 Citations1982D. S. Poskitt, A. R. Tremayne
Journal of the Royal Statistical Society Series B (Statistical Methodology)Precision, Complexity and Bayesian Model Determination
32 Citations1987D. S. Poskitt
Australian Journal of StatisticsTHE CONVERGENCE OF AUTOCORRELATIONS AND AUTOREGRESSIONS1
27 Citations1983E. J. Hannan, L. Kavalieris
BiometrikaA modified Hannan—Rissanen strategy for mixed autoregressive-moving average order determination
22 Citations1987D. S. Poskitt
Journal of Time Series AnalysisESTIMATION OF AUTOREGRESSIVE MOVING‐AVERAGE ORDER GIVEN AN INFINITE NUMBER OF MODELS AND APPROXIMATION OF SPECTRAL DENSITIES
22 Citations1990Benedikt M. Pötscher
A modification of the minimum Akaike information criterion (AIC) procedure for order estimation in autoregressive moving‐average (ARMA) models is introduced so that consistency for the order estimators obtained via this procedure can be established without restricting attention to only a finite number of models.
Elsevier eBooksLATTICE METHODS IN SPECTRAL ESTIMATION**This work was supported in part by the Advanced Research Projects Agency and monitored by RADC/EEV under contract number F19628-78-C-0136.
16 Citations1981John Makhoul
The lattice structure offers a convenient visual realization of the Levinson recursion used in solving the Yule-Walker equations, which focuses on the importance of the lattice as a tool in spectral estimation.
BiometrikaA comparison of estimation methods for vector linear time series models
13 Citations1977D. F. Nicholls