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Nonlinearity testing and modeling for threshold moving average models

Author

Listed:
  • Rubing Liang
  • Cuizhen Niu
  • Qiang Xia
  • Zhiqiang Zhang

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.

Suggested Citation

  • Rubing Liang & Cuizhen Niu & Qiang Xia & Zhiqiang Zhang, 2015. "Nonlinearity testing and modeling for threshold moving average models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2614-2630, December.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:12:p:2614-2630
    DOI: 10.1080/02664763.2015.1043872
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    References listed on IDEAS

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    1. Baragona, R. & Battaglia, F. & Cucina, D., 2004. "Fitting piecewise linear threshold autoregressive models by means of genetic algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 277-295, September.
    2. Dong Li, 2012. "A note on moving-average models with feedback," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(6), pages 873-879, November.
    3. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
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