In statistical applications it is usual to postulate a single hypothetical distribution for modeling the data generating process. However, this practice it is not realistic when the true distribution can change through the input domain (e.g. time). In this work we propose a technique for modelling the possible heterogeneity of time series. Firstly, we include model selection as part of the likelihood maximisation in the main estimation problem; we use both Yeo-Johnson transformations and the hypemormal distribution and compare the results of each. Then, we generalise the above proposal applying it to each instant of time. In this way we can postulate and estimate a pattern of temporal change in the distribution model using an auto-regressive structure to model its evolution. In this early stage of our research we consider lineal models for this evolution and focus on the problem of the prediction of heteroskedastic time series, — although there is no reason why the method cannot be applied to more general regression problems.

The proposed technique is evaluated with daily return series for several stock market indices, improving the results obtained when heterogeneity is not assumed.