Covariance matrix theorems for estimators of time series models: With applications to active tracking problems

Unwin, Judith Mary

(1984)

Unwin, Judith Mary (1984) Covariance matrix theorems for estimators of time series models: With applications to active tracking problems.

Our Full Text Deposits

Full text access: Open

10097555.pdf - 3.62 MB

Abstract

In this thesis, covariance matrices and generalised variances for maximum likelihood estimators of Gaussian autoregressive moving average time series models are derived. It is shown that estimators for pure moving average and pure autoregressive models have covariance matrices which are expressed in terms of two triangular matrices. Furthermore, the generalised variance is obtained from a factorisation of the determinant of the covariance matrix into four constituent parts. Examples of these theorems are given. The results are generalised for estimators of a mixed autoregressive moving average model in which there is either just one moving average parameter or just one autoregressive parameter. In particular the generalised variance is factorised into the determinants of the covariance matrices for efficient estimators of the parameters of the corresponding two pure models, and two other scalar terms. The submatrices of the covariance matrix for the efficient estimators of the parameters of the general mixed model are found by specifying four or five upper triangular matrices, whose non-zero elements are single parameters of the model, and then carrying out some matrix multiplications and additions. Provided the model is not too large, explicit expressions for the variances and covariances can be obtained. Examples, using mixed models, of these methods are given, and the adequacy of the fitted model is discussed in detail. It is proposed that these theorems enable statistical tests to be applied to problems of active tracking, which, traditionally, are expressed in terms of polynomial-projecting dynamic linear models. The problem of testing for constant velocity is considered in detail. A test based on a generalisation of Student's t test is discussed. Several examples of this test procedure are given.

Information about this Version

This is a Accepted version
This version's date is: 1984
This item is not peer reviewed

Link to this Version

https://repository.royalholloway.ac.uk/items/8f3e54db-a8a5-473f-b37f-86623261d670/1/

Item TypeThesis (Doctoral)
TitleCovariance matrix theorems for estimators of time series models: With applications to active tracking problems
AuthorsUnwin, Judith Mary
Uncontrolled KeywordsStatistics; Pure Sciences; Active; Applications; Covariance; Estimators; Matrix; Models; Problems; Series; Theorems; Time; Time Series; Tracking; Time Series
Departments

Identifiers

ISBN978-1-339-61629-2

Deposited by () on 01-Feb-2017 in Royal Holloway Research Online.Last modified on 01-Feb-2017

Notes

Digitised in partnership with ProQuest, 2015-2016. Institution: University of London, Royal Holloway College (United Kingdom).


Details