Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions

Robust autoregressive modeling and its diagnostic analytics with a COVID-19 related application

Autoregressive models in time series are useful in various areas. In this article, we propose a skew-t autoregressive model. We estimate its parameters using the expectation-maximization (EM) method and develop the influence methodology based on local perturbations for its validation. We obtain the normal curvatures for four perturbation strategies to identify influential observations, and then to assess their performance through Monte Carlo simulations. An example of financial data analysis is presented to study daily log-returns for Brent crude futures and investigate possible impact by the COVID-19 pandemic.

Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution

Autoregressive models have played an important role in time series. In this paper, an autoregressive model based on the skew-normal distribution is considered. The estimation of its parameters is carried out by using the expectation–maximization algorithm, whereas the diagnostic analytics are conducted by means of the local influence method. Normal curvatures for the model under four perturbation schemes are established. Simulation studies are conducted to evaluate the performance of the proposed procedure. In addition, an empirical example involving weekly financial return data are analyzed using the procedure with the proposed diagnostic analytics, which has improved the model fit.