Inference in Hidden Markov Processes Sampled at Discrete Times
Université d'Évry - Departement de Mathematiques; ESSEC Business School - Finance Department; HSBC (Global Markets)
This paper is concerned with the estimation of coefficients of continuous-time hidden Markov models when the observations are sampled at discrete times, with a view towards financial applications. These estimates are commonly computed from discretely and frequently-sampled returns. However, recent findings indicate that these estimators are not robust when the frequency increases due to market microstructure. The present work attempts to reconcile continuous-time modeling and discret-time observations. To this end, we propose a model where all the coefficients of the asset log-price Y are unobservable and follow a Markov process X, which represents the hidden market factors which affect Y. We also suppose that stock prices are observed only discretely at random times T. Under the above setting, the inference problem can be treated as a non-linear filtering problem for X by considering measurements given by the random measure associated to (T(k),Y(k))(k0) From a numerical perspective, we develop and compare optimization methods by means of maximum likelihood and Bayesian paradigm so as to compute the state and parameters estimates. Eventually, we provide empirical evidence of the performance of these approaches on simulated and empirical data sets of index returns.
Keywords: Estimation, hidden Markov model, non-linear filter, multivariate point process, likelihood inference, particle systems
JEL Classification: G12, G14, D52, D83
Date posted: August 1, 2005