What is Model Selection

Time series exhibiting seasonal behavior are common in areas such as environmental sciences and economics. Given the current capabilities to generate and store large amounts of data, in particular seasonal time series recorded at a large number of time points, new modeling and computational challenges arise. This article addresses statistical model selection for such big seasonal time series data as follows. A small sample of model orders is obtained, the corresponding time series models are fitted, and an information criterion for each of them is computed. Kriging-based methods are used to emulate the information criterion at any new set of model orders, followed by an efficient global optimization (EGO) algorithm to identify the optimal orders, thus selecting the model. Both simulated and real seasonal big time series data are used to illustrate the method, showing that the model orders are accurately and efficiently identified.