Modellering av finansiella data med dolda markovmodeller / Analysis of Financial Data with Hidden Markov Models

Sammanfattning: The prediction and understanding of market fluctuations are of great interest in today’s society. A common tool for analyzing financial data is the use of different statistical models. This report will focus on examining the stability of a financial data sequence using a statistical model. The sequence that will be used in the report is the logarithmic return of OMXS30 index between the 30th of March 2005 and the 6th of March 2009. The statistical model that will be used is a HMM ( Hidden Markov Model). This model consists essentially of two stochastic processes:  A non-observable Markov chain in a finite state space.  A state-dependent process with a superimposed white noise. The latter of these two processes is generally known. Therefore, the key is to find how the hidden Markov chain behaves. This will be solved with the so-called EM-algorithm, which is an iterative method to get the model to converge. An optimization of the model with respect to the number of states will be made with the BIC (Bayesian Information Criterion). Thereafter, a validation of the model is done by graphically comparing the quantiles of the model distribution function and the given data. This study shows that by employing an HMM it is possible to describe how the return on the index varies, by examining the probability of changes between the Markov chains volatility states.