Nonlinear modeling of time series using Multivariate Adaptive Regression Splines (MARS)
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Authors
Lewis, Peter A. W.
Stevens, James G.
Subjects
Multivariate adaptive regression splines
nonlinear time series models
regression splines
threshold models
ASTAR models
limit cycles
recursive partitioning
Wolf sunspot numbers
nonlinear time series models
regression splines
threshold models
ASTAR models
limit cycles
recursive partitioning
Wolf sunspot numbers
Advisors
Date of Issue
1990-04
Date
1990-04
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
MARS (Multivariate Adaptive Regression Splines) is a new methodology, due to Friedman, for nonlinear regression modeling. MARS can be conceptualized as a generalization of recursive partitioning that uses spline fitting in lieu of other simple functions. Given a set of predictor variables, MARS fits a model in a form of an expansion of product spline basis functions of predictors chosen during a forward and backward recursive partitioning strategy. MARS produces continuous models for discrete data that can have multiple partitions and multilinear terms. Predictor variable contributions and interactions in a MARS model may be analyzed using an ANOVA style decomposition. By letting the predictor variables in MARS be lagged values of a time series, one obtains a new method for nonlinear autoregressive threshold modeling of time series. A significant feature of this extension 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 satisfying behavior for any model of a time series with periodic behavior. Analysis of the Wolf sunspot numbers with MARS appears to give an improvement over existing nonlinear Threshold and Bilinear models
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS-55-90-10
Sponsors
Chief of Naval Research, Arlington, VA
Funder
O&MN, Direct Funding
Format
Citation
Distribution Statement
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.