Time series modelling using multivariate adaptive regression splines and conic quadratic programming

This dissertation investigates the use of adaptive spline treshold autoregression (ASTAR), due to Stevens (1991), which was developed using multivariate adaptive regression splines (MARS), due to Friedman (1991), and use of conic ASTAR (C-ASTAR) which was obtained using conic quadratic programming (CQP).MARS, a modern technology in statistical learning, has importance in regression and classification. MARS is very useful for high dimensional problems and shows a great promise for fitting nonlinear multivariate functions. MARS technique does not impose any particular class of relationship between the predictor variables and outcome variable of interest. In other words, a special advantage of MARS lies in its ability to estimate the contribution of the basis functions so that both the additive and interaction effects of the predictors are allowed to determine the response variable.By letting the predictor variables in the MARS algorithm be lagged values of a time series system, one obtains a univariate ASTAR model for nonlinear autoregressive threshold modeling and analysis of time series, thereby extending the threshold autoregression (TAR) time series methodology developed by Tong. ASTAR consists of two complementary algorithms as MARS. To estimate the model function, as MARS algorithm, ASTAR has two stepwise algorithms which provide to determinate basis functions stand in the model and to get best appropriate model. Because the model obtained with forward stepwise algorithm used in the first step has very complex structure in the second step using backward stepwise algorithm basis functions remove in turn to reach optimum model.In this study a new approach developed by Taylan ve ark. (2010) was applied for the second stepwise algorithm of ASTAR. With this approach ASTAR model turned to Tikhonov regularization problem was transformed to CQP problem. When bounds of this optimization problem are determined using multiobjective optimization approach, too many solutions can be obtained. Thus, it is aimed to attain optimum solution.Moreover, in this study, regression model for time series is emphasized and is supplied to apply time series by deleting deficiencies of it (People Emich 2010).In conclusion, regression model, ASTAR algorithm and C-ASTAR algorithm were applied to two different data sets and these three approaches performances were compared by using different measures.Key Words: Time series, Multivariate adaptive regression splines (MARS), Adaptive splines treshold autoregression (ASTAR), Tikhonov regularization, Multiobjective optimization, Conic quadratic programming (CQP).