Rollage: Efficient Rolling Average Algorithm to Estimate ARMA Models for Big Time Series Data

We develop a new efficient algorithm for the analysis of large-scale time series data. We firstly define rolling averages, derive their analytical properties, and establish their asymptotic distribution. These theoretical results are subsequently exploited to develop an efficient algorithm, called Rollage, for fitting an appropriate AR model to big time series data. When used in conjunction with the Durbin's algorithm, we show that the Rollage algorithm can be used as a criterion to optimally fit ARMA models to big time series data. Empirical experiments on large-scale synthetic time series data support the theoretical results and reveal the efficacy of this new approach, especially when compared to existing methodology.