Emperical Study on Various Symmetric Distributions for Modeling Time Series

TL;DR

This paper compares various symmetric probability distributions, including Pearson type VII and generalized Laplace, for modeling time series with structural changes, highlighting their effectiveness and stability.

Contribution

It provides an empirical evaluation of different symmetric distributions, identifying the Pearson type VII and extended Laplace as more reliable for modeling complex time series.

Findings

Pearson type VII distribution is versatile for time series modeling.

Generalized Laplace performs comparably or better in likelihood and AIC.

Mixture models show potential but lack stability.

Abstract

This study evaluated probability distributions for modeling time series with abrupt structural changes. The Pearson type VII distribution, with an adjustable shape parameter $b$, proved versatile. The generalized Laplace distribution performed similarly to the Pearson model, occasionally surpassing it in terms of likelihood and AIC. Mixture models, including the mixture of $\delta$-function and Gaussian distribution, showed potential but were less stable. Pearson type VII and extended Laplace models were deemed more reliable for general cases. Model selection depends on data characteristics and goals.