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.

在本研究中，我们通过 COVID-19 大流行下的金融应用程序提供了一个激励性示例，以研究自回归 (AR) 建模及其基于不对称分布的诊断。这项工作的目标是： (i) 制定不对称 AR 模型及其估计和诊断；(ii) 评估这些模型的参数估计器和局部影响技术的性能；(iii) 提供一种工具来展示如何分析在 AR 结构下遵循不对称分布的数据。我们利用偏正态分布的随机表示的优势，通过期望最大化算法有效地估计相应 AR 模型的参数。通过使用具有四种扰动方案的局部影响技术进行诊断分析。通过使用蒙特卡罗模拟，我们评估了相应估计器和局部影响技术的统计行为。使用当前工作中引入的方法分析了截至 2020 年更新的财务数据的插图，作为有效应用的示例，从中可以解释 COVID-19 大流行的非典型病例。