Browsing by Author "Lapinlampi, George"

There’s a specific but sometimes quite a significant problem in time series modeling caused by changing means. First, the foundation behind the model addressing this problem is introduced in the form of the basic theory of Markov chains and problems related to hidden Markov chains. This approach builds on the ARMA (Autoregressive Moving average) model but is utilizing estimation methods from the areas not specifically dedicated to the time series analysis. The hybrid approach comprising Markov chains, EM (expectation-maximization) algorithm, and linear modeling may be well justified when the conventional methods do not seem to produce desired results and the modeler has competencies and means to attempt more sophisticated approaches. The literature review provides an insight into an earlier kind of models that have led to the development of the model investigated in this work. Finally, in the empirical part the model’s power is assessed against the conventional ARMA model. The modeling is performed on the simulated series in order to assess the functionality of the EM algorithm, to have a precise knowledge about real state variables, and to get an optimal comparison between a linear and non-linear models. The models are compared using multiple diagnostic procedures such as AIC (Akaike criterion), autocorrelation and partial autocorrelation functions, residuals variance, and other descriptive statistical measures.