Title: A multimomental ARMA model: Initial formulation and a case study
Authors: Thomas Michael Bartlett - University of Campinas (Brazil) [presenting]
Levy Boccato - University of Campinas (Brazil)
Abstract: Recently, nonnormal distribution functions have been developed to model more precisely and richly the behavior of time series of data. We aim at developing a times series model that describes, by mixing Gaussian distributions, the evolution of each statistical moment up to the third order - mean, variance and skewness. To each instant of time and to each moment an ARMA law of evolution is applied and the estimation of the model is done by optimizing a quasi likelihood function that depends on the ARMA coefficients of the three moments. Thus, the method of moments for Gaussian mixtures is used to obtain a probability density function which has the desired instantaneous moments. Employing Newton Method and Nelder-Mead optimization procedures to estimate the model, an empirical analysis is done studying the model's performance and consistency using a synthetic time series.