An investigation of multivariate adaptive regression splines for modeling and analysis of univariate and semi-multivariate time series systems
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Authors
Stevens, James G.
Subjects
Adaptive regression splines
Threshold autoregression
Time series systems
Simulation
Model selection
Threshold autoregression
Time series systems
Simulation
Model selection
Advisors
Lewis, Peter A.W.
Date of Issue
1991-09
Date
September 1991
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
This dissertation investigates the use of multivariate adaptive regression splines (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 uses 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. The model seem well suited for taking into account the complex interactions among multivariate, cross-correlated, lagged predictor variables of a time series system. A significant feature of this time series application of MARS is its ability to produce models with limit cycles when modeling time series data that exhibit periodic behavior. In a physical context, limit cycles represent a stationary state of sustained oscillations. A difficulty faced during regression modeling is the problem of model selection, i.e., choosing the appropriate model dimension and model predictable variables. Currently, a modified form of generalized cross-validation (GCV*), first suggested by Craven and Wahba, is used for model selection within the MARS algorithm. However, one question that immediately develops is whether GCV* Is the 'best' criterion for model selection when using serially and cross-correlated time series data. Using MSE as a measure of performance, simulations show that othr model selection criteria, in particular, the Schwarz-Rissanen (SC) criterion can improve model election over GCV*).
Type
Thesis
Description
Series/Report No
Department
Department of Operations Research
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
192 p.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.