Mixtures of Distributions and Volatility: A Theoretical Explanation

We generate a time series with the following characteristics using Monte Carlo methods: a) series with distributions that are a combination of the two normal distributions with different variances, b) series that satisfy volatility models, c) series that satisfy an AR(1) model but with contaminated errors which 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. We can see from the analysis that identifying the actual generation mechanism of the series in practise is difficult. In fact, the processes resulting from distribution mixes are very similar to the ones that satisfy the volatility scheme. We use the usual tools in the identification phase of any time series, such as series diagrams, histograms, the corresponding sampling distributions, correlograms, and partial correlograms, as well as the corresponding theoretical considerations.