Abstract
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.
Highlights
For time series data analysis, autoregressive (AR) modeling is an essential technique and has been applied in many areas including biology, chemistry, earth sciences, economics, education, engineering, finance, health, medicine, and physics; see, for example, [1,2] for recent accounts of time series modeling and applications
Diagnostic analytics is used in a number of regression and time series models
Twenty-four influential observations are detected by the local influence diagnostic analytics under the SN distribution, which is more than the twenty influential values detected by the local influence analytics under the normal distribution
Summary
For time series data analysis, autoregressive (AR) modeling is an essential technique and has been applied in many areas including biology, chemistry, earth sciences, economics, education, engineering, finance, health, medicine, and physics; see, for example, [1,2] for recent accounts of time series modeling and applications. Local influence diagnostics is the study of how relevant minor perturbations impact the fit of the model and the results of statistical inference. In order to deal with such data, the skew-normal (SN) distribution and its scale-mixtures have provided an appealing alternative and can be adopted Their properties, extensions, and applications are becoming increasingly popular; see [19,20,21,22,23,24,25,26]. The objective of the present paper is to formulate an AR model under the SN distribution (SN AR model) and to derive diagnostic analytics with applications to financial data. The derivations of the normal curvatures are presented in the Appendix A
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