Functional coefficient autoregressive models: estimation and tests of hypotheses

Rong Chen, Lon Mu Liu

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


In this paper, we study nonparametric estimation and hypothesis testing procedures for the functional coefficient AR (FAR) models of the form Xt = f1(Xt-d)Xt-1 + ⋯ + fp(Xt-d)Xt-p + εt, first proposed by Chen and Tsay (1993). As a direct generalization of the linear AR model, the FAR model is a rich class of models that includes many useful parametric nonlinear time series models such as the threshold AR models of long (1983) and exponential AR models of Haggan and Ozaki (1981). We propose a local linear estimation procedure for estimating the coefficient functions and study its asymptotic properties. In addition, we propose two testing procedures. The first one tests whether all the coefficient functions are constant, i.e. whether the process is linear. The second one tests if all the coefficient functions are continuous, i.e. if any threshold type of nonlinearity presents in the process. The results of some simulation studies as well as a real example are presented.

Original languageEnglish (US)
Pages (from-to)151-173
Number of pages23
JournalJournal of Time Series Analysis
Issue number2
StatePublished - Mar 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Continuity test
  • Linearity test
  • Local linear estimation
  • Nonparametric estimation
  • One-sided kernel
  • Threshold model


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