Annals of the Institute of Statistical Mathematics

, Volume 51, Issue 4, pp 691–706

Multivariate Local Polynomial Fitting for Martingale Nonlinear Regression Models

  • Zhan-Qian Lu

DOI: 10.1023/A:1004083213922

Cite this article as:
Lu, ZQ. Annals of the Institute of Statistical Mathematics (1999) 51: 691. doi:10.1023/A:1004083213922


Local polynomial modelling is a useful tool for nonlinear time series analysis. For nonlinear regression models with martingale difference errors, this paper presents a simple proof of local linear and local quadratic fittings under apparently minimal short-range dependence condition. Explicit formulae for the asymptotic bias and asymptotic variance are given, which facilitate numerical evaluations of these important quantities. The general theory is applied to nonparametric partial derivative estimation in nonlinear time series. A bias-adjusted method for constructing confidence intervals for first-order partial derivatives is described. Two examples, including the sunspots data, are used to demonstrate the use of local quadratic fitting for modelling and characterizing nonlinearity in time series data.

Partial derivative estimation nonlinearity in time series confidence intervals nonparametric estimation sunspots data 

Copyright information

© The Institute of Statistical Mathematics 1999

Authors and Affiliations

  • Zhan-Qian Lu
    • 1
  1. 1.Department of MathematicsThe Hong Kong University of Science and TechnologyHong KongChina

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