NONLINEAR MODELING OF TIME-SERIES USING MULTIVARIATE ADAPTIVE REGRESSION SPLINES (MARS)

被引:140
作者
LEWIS, PAW [1 ]
STEVENS, JG [1 ]
机构
[1] USA,WASHINGTON,DC 20310
关键词
ASTAR MODELS; LIMIT CYCLES; NONLINEAR TIME SERIES MODELS; RECURSIVE PARTITIONING; THRESHOLD MODELS; WOLF SUNSPOT NUMBERS;
D O I
10.2307/2290499
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Multivariate Adaptive Regression Splines (MARS) 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 fitting functions. Given a set of predictor variables, MARS fits a model in the form of an expansion in product spline basis functions of predictors chosen during a forward and backward recursive partitioning strategy. MARS produces continuous models for high-dimensional data that can have multiple partitions and predictor variable interactions. 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 yearly Wolf sunspot numbers with MARS appears to give an improvement over existing nonlinear threshold and bilinear models. A graphical representation for the models is given.
引用
收藏
页码:864 / 877
页数:14
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