Change point dynamics for financial data: an indexed Markov chain approach

This paper uses an Indexed Markov Chain to model high frequency price returns of quoted rms. Introducing an Index process permits consideration of endogenous market volatility, and two important stylized facts of financial time series can be taken into account: long memory and volatility clustering. This paper rst proposes a method to optimally determine the state space of the Index process, which is based on a change-point approach for Markov chains. Furthermore, we provide an explicit formula for the probability distribution function of the rst change of state of the Index process. Results are illustrated with an application to intra-day firm prices.