A new approach to adaptive spline threshold autoregression by using Tikhonov regularization and continuous optimization

Abstract

In this study adaptive spline threshold autoregression and conic quadratic programming is used to develope conic adaptive spline threshold autoregression. With the introduced approach the second stepwise algorithm of adaptive spline threshold autoregression model turned to the Tikhonov regularization problem which was transformed into conic quadratic programming problem. The aim is to attain an optimum solution chosen in many solutions obtained by determining the bounds of the optimization problem using multiobjective optimization approach. Furthermore, in application part we used two different data set to compare performances of linear regression, adaptive spline threshold autoregression and conic adaptive spline threshold autoregression approaches.

Subject Classification: (2010):

• 62M10
• 62J07
• 90C20

Keywords:

• Time series
• Multivariate adaptive regression splines (MARS)
• Adaptive splines threshold autoregression (ASTAR)
• Tikhonov regularization
• Multiobjective optimization
• Conic quadratic programming (CQP)

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.