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Joint detection for functional polynomial regression with autoregressive errors

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  • Tao Zhang
  • Pengjie Dai
  • Qingzhao Zhang

Abstract

In this article, we are concerned with detecting the true structure of a functional polynomial regression with autoregressive (AR) errors. The first issue is to detect which orders of the polynomial are significant in functional polynomial regression. The second issue is to detect which orders of the AR process in the AR errors are significant. We propose a shrinkage method to deal with the two problems: polynomial order selection and autoregressive order selection. Simulation studies demonstrate that the new method can identify the true structure. One empirical example is also presented to illustrate the usefulness of our method.

Suggested Citation

  • Tao Zhang & Pengjie Dai & Qingzhao Zhang, 2017. "Joint detection for functional polynomial regression with autoregressive errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 7837-7854, August.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:16:p:7837-7854
    DOI: 10.1080/03610926.2015.1096384
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