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Title: On gradual regime switching models : a generalisation of Hamilton's method of time-series analysis
Author: Bodger, Owen Galdan
Awarding Body: University of Wales, Swansea
Current Institution: Swansea University
Date of Award: 2005
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The class of Markov Switching time series models, introduced by Professor James Hamilton, is nearly twenty years old. Despite this, relatively little work has been done on allowing gradual transitions between the regimes of the model. Almost all of the published work relates to modelling a transition between two regression lines rather than incorporating it into a time series model. We decided to approach the problem from two directions. First, we wanted to look at Filtered Telegraph signals (Filtered Markov processes) and consider their suitability for time series analysis. Secondly, we wished to extend the existing Regime Switching models to allow a gradual transition between regimes. In our work on the Filtered Markov process we present a method for obtaining moments for a signal with any number of regimes, rather than the usual two. This enables us to find the stationary, transient and conditional moments of the signal. We include an expression for the covariance of two observations from a signal, obtained using the conditional moments. While considering how to fit a Filtered Markov process we identify several new methods that can be used for estimating the parameters of a sample from the Beta distribution where the observations have been contaminated by noise. We also include extensive tables of the percentiles of the estimators for each of the methods. We also present a new algorithm that utilises the Filtered Markov process to generate random Beta variates. Finally we take a more practical approach, introducing some simple models that, while useful in their own right, could also be used to bridge the gap between the two-regime Markov switching model and the Filtered Markov process. These Ladder models are then applied to several data sets to explore the problems faced by gradual switching models and collect evidence of their suitability.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available