Copula based Model Correction for Bivariate Bernoulli Financial Series

In this paper we address the problem of simultaneously modeling two financial series of the daily returns' direction (up/down variation) of an asset. We describe jointly both series by using a new family of Markov models called Partition Markov Models. This family has the characteristic of finding a Markov model with a minimal number of parameters. However, sometimes the sample size does not allow to extract enough information about the model. Then, we develop a copula based methodology to correct the joint probabilities by using the marginal models obtained by the Partition Markov Models.