Summary:
In the context of this thesis, the discrete semi-Markov models will be presented, so as
to connect them thereafter with the hidden semi Markov models. After this presentation,
statistics estimations methods with basic tool the EM algorithm (for whom a brief description
is given) will be pointed out. A detailed presentation of the latter, under specific assumptions
whether on component distribution or on sojourn time distribution in hidden states, is
followed. In particular, observation component distribution such as normal and student are
under review, whereas, as far as for the sojourn time in hidden states are concerned, negative
binomial is examined. Finally, hidden semi markov models are fitted in the prices of index
SnP 500 exploring how effectively these models reproduce the stylized facts that Granger and
Ding pointed out.
Keywords:
Markov,Semi-Markov,time series,
