Functional coefficient autoregressive models for vector time series

• Published in: Computational statistics & data analysis Vol. 50; no. 12; pp. 3547 - 3566
• Main Authors: Harvill, Jane L., Ray, Bonnie K.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2006; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Exact sciences and technology; General topics; Inference from stochastic processes; time series analysis; Mathematics; Multivariate analysis; Multivariate series; Nonlinearity; Nonparametric regression; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Sciences and techniques of general use; Sieve likelihood bootstrap test; Statistics; Nonlinearity; Sieve likelihood bootstrap test; Multivariate series; Nonparametric regression; Data analysis; Time series; Autoregressive model; Multivariate analysis; Kernel method; Functional; Kernels; Statistical regression; Statistical computation; Simulation; Regression model; Non linear model; Bootstrap; Test power; Autoregressive processes
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2005.07.016

We extend the functional coefficient autoregressive (FCAR) model to the multivariate nonlinear time series framework. We show how to estimate parameters of the model using kernel regression techniques, discuss properties of the estimators, and provide a bootstrap test for determining the presence of nonlinearity in a vector time series. The power of the test is examined through extensive simulations. For illustration, we apply the methods to a series of annual temperatures and tree ring widths. Computational issues are also briefly discussed.