Mixtures of Distributions and Volatility

Abstract

Using Monte Carlo methods we generate time series with the following features: a) series with distributions that are the mix of two normal distributions with different variances, b) series that satisfy volatility models, c) series that satisfy an AR(1) model but with contaminated errors that follow the same distribution as the mixes given in a) and d) series that follow the same distribution as the mixes given in a) but with conditional heterocedasticity. From the analysis we see that it is difficult to identify in practical situations the real generating process of the series. In fact, the processes that come from distribution mixes have many similar characteristics to the ones that satisfy the volatility scheme. We use the corresponding theoretical considerations and also the usual tools in the identifying process of any time series; that is, series graphs, histograms, the corresponding sampling distributions, correlograms and partial correlograms.