I. Introduction
The problem of analyzing financial time series data is an important task for both financial research and investment. In the past decades, many researchers take the modeling approach to describe financial data. Modeling provides us a way of discovering knowledge from data and making predictions [1]. From this point, modeling financial time series data is very similar to modeling signals in engineering applications. For example, in the presence of noise, filtering methods such as Kalman filters and particle filters can be applied to financial data [2], [3]. With the recent development of Bayesian nonparametric modeling in signal processing community, we can model financial data with more flexible tools and modeling methods, such as Gaussian process (GP) [4] and copula process [5], etc.