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Activity Number:
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308
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Type:
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Contributed
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Date/Time:
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Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
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Sponsor:
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Business and Economics Statistics Section
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| Abstract - #300809 |
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Title:
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Functional Coefficient Regression Models with Dependent Data
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Author(s):
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Yanrong Cao*+ and Haiqun Lin and Zhou Wu and Yan Yu
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Companies:
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University of Toronto and Yale University and University of Cincinnati and University of Cincinnati
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Address:
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Joseph L. Rotman School of Management, Toronto, ON, M5S 3E6, Canada
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Keywords:
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multivariate time series ; functional coefficient regression model ; dimensionreduction ; forecasting ; consistency ; asymptotics
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Abstract:
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A penalized spline (PS) approach is proposed to estimate functional coefficient (FC) regression models for nonlinear time series (TS). FC regression models assume regression coefficients vary with certain lower dimensional covariates, providing appreciable flexibility in capturing the underlying dynamics in data and avoiding the so-called "curse of dimensionality" in multivariate nonparametric TS estimation. One of the appeals of our PS approach lies in the efficiency in estimating coefficient functions via the global smoothing method. In addition, enabled by assigning different penalties accordingly, different smoothness is allowed for different functional coefficients. Penalty terms, selected by minimizing generalized cross-validation scores (GCV), balance the goodness-of-fit and smoothness. The number and location of knots are no longer crucial if the minimum number of knots is reached. Consistency and asymptotic normality of the penalized least squares estimators are obtained. Our PS approach also enables multi-step-ahead forecasting with an explicit model expression in contrast to the local smoothing method. Both simulation examples and a real data application are demonstrated.
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