Dependent and Independent Time Series

TL;DR

This paper develops a new time series theory based on elliptical distributions that models dependence between errors, challenging traditional hierarchical models like GARCH and highlighting the importance of model selection criteria.

Contribution

It introduces a likelihood-based approach for dependent samples in time series, extending elliptical models and criticizing the effectiveness of hierarchical models under this framework.

Findings

Hierarchical models show insignificant relevance under the new approach.

Dependent probabilistic samples provide a different perspective on volatility modeling.

The modified BIC criterion emphasizes the difficulty of model differentiation.

Abstract

The time series theory is set in this work under the domain of general elliptically contoured distributions. The advent of a time series approach that is in accordance with the expected reality of dependence between errors, transfers the increasingly complex and difficult to handle correlation analysis into a discipline that models volatility from a new view of a likelihood based on dependent probabilistic samples. The equally important problem of model selection is strengthened, but at the same time criticized with the introduction of degrees of evidence of significant difference in the modified BIC criterion . The demanding scale of differentiation puts a well-known database in trouble by observing insignificant relevance between the hierarchical models most used in the theory of time series under independence, such as Arch, Garch, Tgarch and Egarch. For extreme cases where the probabilistic independence of the samples is exceptionally demonstrated by an expert, the article also proposes the theory of time series under elliptical models, but with the same demanding comparison of the degrees of evidence of differences of the modified BIC. The example studied under this approach also does not denote any advantage of the hierarchical models studied. Such a new perspective for a likelihood based on dependent probabilistic samples has arisen naturally in similar context in finance under the setting of multivector variate distributions.