Physical Sciences and Mathematics Commons^™

Seasonal Decomposition For Geographical Time Series Using Nonparametric Regression, Hyukjun Gweon

Electronic Thesis and Dissertation Repository

A time series often contains various systematic effects such as trends and seasonality. These different components can be determined and separated by decomposition methods. In this thesis, we discuss time series decomposition process using nonparametric regression. A method based on both loess and harmonic regression is suggested and an optimal model selection method is discussed. We then compare the process with seasonal-trend decomposition by loess STL (Cleveland, 1979). While STL works well when that proper parameters are used, the method we introduce is also competitive: it makes parameter choice more automatic and less complex. The decomposition process often requires that …

Model Selection With Information Criteria, Changjiang Xu

Electronic Thesis and Dissertation Repository

This thesis is on model selection using information criteria. The information criteria include generalized information criterion and a family of Bayesian information criteria. The properties and improvement of the information criteria are investigated.

We analyze nonasymptotic and asymptotic properties of the information criteria for linear models, probabilistic models, and high dimensional models, respectively. We give probability of selecting a model and compute the probability by Monte Carlo methods. We derive the conditions under which the criteria are consistent, underfitting, or overfitting.

We further propose new model selection procedures to improve the information criteria. The procedures combine the information criteria with …