Asymmetric autoregressive models: statistical aspects and a financial application under COVID-19 pandemic

J Appl Stat. 2021 Apr 24;49(5):1323-1347. doi: 10.1080/02664763.2021.1913103. eCollection 2022.

Abstract

In the present study, we provide a motivating example with a financial application under COVID-19 pandemic to investigate autoregressive (AR) modeling and its diagnostics based on asymmetric distributions. The objectives of this work are: (i) to formulate asymmetric AR models and their estimation and diagnostics; (ii) to assess the performance of the parameters estimators and of the local influence technique for these models; and (iii) to provide a tool to show how data following an asymmetric distribution under an AR structure should be analyzed. We take the advantages of the stochastic representation of the skew-normal distribution to estimate the parameters of the corresponding AR model efficiently with the expectation-maximization algorithm. Diagnostic analytics are conducted by using the local influence technique with four perturbation schemes. By employing Monte Carlo simulations, we evaluate the statistical behavior of the corresponding estimators and of the local influence technique. An illustration with financial data updated until 2020, analyzed using the methodology introduced in the present work, is presented as an example of effective applications, from where it is possible to explain atypical cases from the COVID-19 pandemic.

Keywords: Expectation-maximization algorithm; Monte Carlo simulation; local influence; maximum likelihood methods; non-normality; times-series models.

Grant support

The research of Y. Liu was supported by the Natural Science Foundation of China [grant number 11271259]. The research of V. Leiva was partially supported by the National Agency for Research and Development (ANID) of the Chilean government [grant number FONDECYT 1200525].