A Sequential and Iterative Testing Procedure to Identify the Nature of a Time Series Generating Process

Abstract

An inferential approach is proposed to identify the nature of the generating process corresponding to a real time series. This new sequential and iterative testing procedure goes beyond the Box and Jenkins methodology for the identification, estimation, and validation of linear data generating processes by investigating the probabilistic structure of non-Gaussian estimated residuals {ϵ _t } for the possible presence of nonlinear serial dependence. The testing procedure aims at indicating the right type of dependence present in a series by means of specific inferential tests on the moments of the generating structure probability distribution. The test statistics adopted are very popular and powerful and encompass a wide range of stochastic nonlinearity alternatives. The U.S. Industrial Production Index series is used to illustrate the iterative testing procedure proposed.

Keywords:

• Conditional probability
• Inferential testing
• Nonlinear serial dependence
• Sequential and iterative procedure

2000 Mathematics Subject Classification:

• 60G07
• 62L10
• 62M10
• 91B84

ACKNOWLEDGMENTS

The authors thank the Editor-in-Chief, Professor Nitis Mukhopadhyay, and the Associate Editor for helpful comments and remarks on the layout of this manuscript. The first author gratefully acknowledges the research grant received from the Italian Ministry of Education, University and Research.

This study was made when the author was a student at the University of Bologna and does not necessarily represent the view of the organization to which she is affiliated.

Notes

Note: * and ** indicate significance at 5% and 1%, respectively.

Recommended by N. Mukhopadhyay