Emperical Study on Various Symmetric Distributions for Modeling Time Series

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.