Functional-coefficient regression models for nonlinear time series

Zongwu Cai, Jianqing Fan, Qiwei Yao

Research output: Contribution to journalArticlepeer-review

435 Scopus citations


The local linear regression technique is applied to estimation of functional-coefficient regression models for time series data. The models include threshold autoregressive models and functional-coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance. Also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross-validatory estimation for the expected forecasting errors. The proposed methodology is data-analytic and of sufficient flexibility to analyze complex and multivariate nonlinear structures without suffering from the “curse of dimensionality.” The asymptotic properties of the proposed estimators are investigated under the α-mixing condition. Both simulated and real data examples are used for illustration.

Original languageEnglish (US)
Pages (from-to)941-956
Number of pages16
JournalJournal of the American Statistical Association
Issue number451
StatePublished - Sep 1 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Asymptotic normality
  • Bootstrap
  • Forecasting
  • Goodness-of-fit test
  • Local linear regression
  • Nonlinear time series
  • Varying-coefficient models
  • α-mixing


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