Emulated order identification for models of big time series data

This interdisciplinary research includes elements of computing, optimization, and statistics for big data. Specifically, it addresses model order identification aspects of big time series data. Computing and minimizing information criteria, such as BIC, on a grid of integer orders becomes prohibitive for time series recorded at a large number of time points. We propose to compute information criteria only for a sample of integer orders and use kriging-based methods to emulate the information criteria on the rest of the grid. Then we use an efficient global optimization (EGO) algorithm to identify the orders. The method is applied to both ARMA and ARMA-GARCH models. We simulated times series from each type of model of prespecified orders and applied the method to identify the orders. We also used real big time series with tens of thousands of time points to illustrate the method. In particular, we used sentiment scores for news headlines on the economy for ARMA models, and the NASDAQ daily returns for ARMA-GARCH models, from the beginning in 1971 to mid-April 2020 in the early stages of the COVID-19 pandemic. The proposed method identifies efficiently and accurately the orders of models for big time series data.