# 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 because of conditional heterocedasticity The analysis shows that determining the actual generation mechanism of the series in practice is difficult. In fact, the processes that emerge from distribution mixes are strikingly similar to those that satisfy the volatility scheme. In the identification phase of any time series, we employ the standard tools such as series diagrams, histograms, the corresponding sampling distributions, correlograms, and partial correlograms, as well as the corresponding theoretical considerations.

Author (S) Details

**Professor Juan Carlos Abril
**Universidad Nacional de Tucumán, Facultad de Ciencias Económicas and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Tucumán, Argentina.

**Professor Juan Carlos Abril
**Universidad Nacional de Tucumán, Facultad de Ciencias Económicas and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Tucumán, Argentina.

**Professor Carlos Ismael Martínez
**Universidad Nacional de Tucumán, Facultad de Ciencias Económicas and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Tucumán, Argentina.

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