Time Series of Correlated Count Data using Multifractal Process

This paper generalizes Poisson-Multifractal for correlated time series of count data. We show that the model has useful properties; it captures long-term time dependence and exible dependence between types of count. Based on real data, the correlated multifractal model is used to model the number of claims of two separate coverages in automobile insurance. Smoothed values of the underlying process can be estimated, and a speci c property of the model allows us to split the unobserved process into separate elements. These elements can be considered as climatic, economic or social factors a ecting the frequency of claims, which can be associated with exogeneous informations. Even if the model proposed in this paper implies dependence between count variables, we think that it can be easily generalized in many directions: to model dependence between claim cost and frequency, or between the claims frequency of di erent insurance products.