Nonlinearity testing and modeling for threshold moving average models

Abstract

In this paper, we suggest a simple test and an easily applicable modeling procedure for threshold moving average (TMA) models. Firstly, based on the fitted residuals by maximum likelihood estimate (MLE) for MA models, we construct a simple statistic, which is obtained by linear arrange regression and follows F-distribution approximately, to test for threshold nonlinearity and specify the threshold variables. And then, we use some scatterplots to identify the number and locations of the potential thresholds. Finally, with the statistic and Akaike information criterion, we propose the procedure to build TMA models. Both the power of test statistic and the convenience of modeling procedure can work very well demonstrated by simulation experiments and the application to a real example.

Keywords:

• arranged regression
• MA model
• the fitted residuals
• nonlinearity test
• AIC
• TMA model

AMS Subject Classification:

• 62F03
• 62F10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Qiang Xia was supported in part by National Social Science Foundation of China (No.12CTJ019), Ministry of Education in China Project of Humanities and Social Sciences (Project No.11YJCZH195), and the National Natural Science Foundation of China (grant no.61375006). The research of Cuizhen Niu was supported by the Outstanding Innovative Talents Cultivation Funded Programs 2014 of Renmin University of China.