Skip to main content
Kent Academic Repository

Aspects of non-linear time series analysis

Moeanaddin, Rahim (1989) Aspects of non-linear time series analysis. Doctor of Philosophy (PhD) thesis, University of Kent. (doi:10.22024/UniKent/01.02.86180) (KAR id:86180)


Some difficulties of non-linear time series modelling are discussed. The importance of likelihood plots and information matrix calculation is demonstrated. A constructive use of reparametrization is illustrated. Possible non-invertibility of two bilinear models fitted to real data is discussed. The relation between the variance of error term and the variance of the estimate of the bilinear term is also studied. We have examined numerical solutions for a recursive relation for computing the rn-step-ahead conditional density of a non-linear autoregressive model by using the Chapman-Kolmogorov formula. The stationary marginal probability density function of the model is approximated by the rn-step-ahead conditional density, for sufficiently large m. The advantage of incorporating the matrix squaring procedure is also studied. The conditional mean (regression function) and conditional variance of some non-linear models are studied briefly .The importance of non-parametric estimation of regression functions in non-linear time series analysis is demonstrated. A comparison of likelihood ratio tests using the newly available asymptotic results with the non-likelihood ratio approach such as the modified Petruccelli-Davies's test and Tsay's test is studied. The 5% empirical critical values for the some cases of likelihood ratio test is also obtained. The• effect of outliers on the tests is briefly studied. The importance of the profile likelihood plots in locating the threshold and estimating the delay parameter is demonstrated. The blowfly data (raw and transformed) analysed. The importance of influential data is also discussed. The non-monotonicity of the conditional variance of the error of a rn-step non-linear least squares predictor is discussed. We have also studied methods of evaluating the conditional variance for non-linear autoregressive models and illustrated these with both real and simulated data. Bias correction is included. Moreover, the possibility of combinations of forecasts is explored. The performances of linear bilinear and SETAR models in predicting the sunspot numbers are compared.

Item Type: Thesis (Doctor of Philosophy (PhD))
DOI/Identification number: 10.22024/UniKent/01.02.86180
Additional information: This thesis has been digitised by EThOS, the British Library digitisation service, for purposes of preservation and dissemination. It was uploaded to KAR on 09 February 2021 in order to hold its content and record within University of Kent systems. It is available Open Access using a Creative Commons Attribution, Non-commercial, No Derivatives ( licence so that the thesis and its author, can benefit from opportunities for increased readership and citation. This was done in line with University of Kent policies ( If you feel that your rights are compromised by open access to this thesis, or if you would like more information about its availability, please contact us at and we will seriously consider your claim under the terms of our Take-Down Policy (
Uncontrolled keywords: Statistics
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
SWORD Depositor: SWORD Copy
Depositing User: SWORD Copy
Date Deposited: 29 Oct 2019 16:32 UTC
Last Modified: 14 Feb 2022 12:16 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.