Investigation of Multivariate Adaptive Regression Splines for Modeling andAnalysis of Univariate and Semi-Multivariate Time Series Systems

摘要

This dissertation investigates the use of multivariate adaptive regressionsplines (MARS), due to Friedman, for nonlinear regression modeling and analysis of time series systems. MARS can be conceptualized as a generalization of recursive partitioning that use spline fitting in lieu of other simple fitting functions. MARS is a computationally intensive methodology that fits a nonparametric regression model in the form of an expansion in product spline basis functions of predictor variables chosen during a forward and backward recursive partitioning strategy. The MARS algorithm produces continuous nonlinear regression models for high-dimensional data using a combination of predictor variable interactions and partitions of the predictor variable space. By letting the predictor variables in the MARS algorithm be lagged values of a time series system, one obtains a univariate (ASTAR) or semi-multivariate (SMASTAR) adaptive spline threshold autoregressive model for nonlinear autoregressive threshold modeling and analysis of time series, thereby extending the threshold autoregression (TAR) time series methodology developed by Tong.