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# Modeling Time Series by Using Multivariate Adaptive Regression Splines (MARS) (Data Sets A,B,C)

DOI link for Modeling Time Series by Using Multivariate Adaptive Regression Splines (MARS) (Data Sets A,B,C)

Modeling Time Series by Using Multivariate Adaptive Regression Splines (MARS) (Data Sets A,B,C) book

# Modeling Time Series by Using Multivariate Adaptive Regression Splines (MARS) (Data Sets A,B,C)

DOI link for Modeling Time Series by Using Multivariate Adaptive Regression Splines (MARS) (Data Sets A,B,C)

Modeling Time Series by Using Multivariate Adaptive Regression Splines (MARS) (Data Sets A,B,C) book

## ABSTRACT

To provide a framework for a regression modeling methodology, let y represent a single univariate response variable tha t depends on a vector of p predictor variables x where x = ( x i , . . . ,x Vi. . . ,x p). Assume we are given N samples of y and x, namely { y i ,x i}^Ll1 and that we can describe y with the regression model,

y = f (x i , . . . , x p) + € (1 )

over some domain D C IRP, which contains the data. The function / (x ) reflects the true but unknown relationship between y and x. The random additive error variable e, which is assumed to have mean zero and variance reflects the dependence of y on quantities other than x. Quoting Friedman (1991b) “/(x ) is taken to be that component of y tha t varies smoothly with changing values of x, whereas the noise is taken to be the leftover part that does not.”