There are many nonlinear econometric models which are useful in analysis of financial time series. In this thesis, we consider two kinds of nonlinear autoregressive models for nonnegative integer-valued time series: threshold autoregressive models and Markov switching models, in which the conditional distribution given historical information is the Poisson distribution. The link between the conditional variance (i.e. the conditional mean for the Poisson distribution) and its past values as well as the observed values of the Poisson process may be different according to the threshold variable in threshold autoregressive models, and to an unobservable state variable in Markov switching models in different regimes. We give a condition on parameters under which the Poisson generalized threshold autoregressive heteroscedastic (PTGARCH) process can be approximated by a geometrically ergodic process. Under this condition, we discuss statistical inference (estimation and tests) for PTGARCH models, and give the asymptotic theory on the inference. The complete structure of the threshold autoregressive model is not exactly specific in economic theory for the most financial applications of the model. In particular, the number of regimes, the value of threshold and the delay parameter are often unknown and cannot be assumed known. Therefore, in this research, the performance of various information criteria for choosing the number of regimes, the threshold value and the delay parameters for different sample sizes is investigated. Tests for threshold nonlinearity are applied. The characteristics of Markovian switching Poisson generalized autoregressive hetero-scedastic (MS-PGARCH) models are given, and the maximum likelihood estimation of parameters is discussed. Simulation studies and applications to modelling financial counting time series are presented to support our methodology for both the PTGARCH model and the MS-PGARCH model.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:618886 |
| Date | January 2014 |
| Creators | Almarashi, Abdullah Maedh |
| Publisher | University of Strathclyde |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=23669 |
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