Big time series data with tens of thousands of time points involve complex statistical modeling. Minimizing Information Criteria (IC), such as AIC, AICC or BIC, is used for model order identification. However, this identification process is computationally intensive for big time series because it depends on the repeated computation of the likelihood function. We propose a computationally efficient IC optimization method based on fast kriging surrogates. First, we apply the method to ARMA models with two orders, then we expand it to seasonal time series models of higher dimensional order space. To demonstrate this method, we analyze the results from both simulated and real big time series data related to appliances energy consumption. The method proposed can speed up the order identification process, but its accuracy and computing time depend on the number of fitted time series models needed for the IC optimization.