**Joseph Tadjuidje Kamgaing**

visiting Charles University of Prague

We consider time series switching between different dynamics or phases, e.g. a
generalized mixture of first order nonlinear AR-ARCH models with two dynamics

The hidden process is a first order Markov chain with values in {0, 1}, the residuals ot are i.i.d. with mean 0 and variance 1, the autoregressive, and , and volatility, and , functions are unknown. We first present some conditions that ensure the asymptotic stability( Geometric Ergodicity) of the process and define a version of the likelihood function under mild assumptions. Further, based on the likelihood we investigate the behavior of feedfoward networks for estimating the autoregressive and volatility functions and identifying the changepoints between different phases.

Since the process is not observable, we design a version of the Expectation Maximization algorithm that account for solving the problem numerically. In fact, this algorithm consists of assuming in the Expectation step that the parameters of the networks functions are known and to estimate the . Considering now the the parameters of the networks functions are derived in theMaximization step. Both steps are iterated until a stopping criterion is satisfied.

Based on these estimations, we construct a trading strategy that we
apply on real life data and compare the results with those of the
classical Buy and Hold strategy.

2005-05-23