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

We develop a new method to estimate an ARMA model in the presence of big time series data. Using the concept of a rolling average, we develop a new efficient algorithm, called Rollage, to estimate the order of an AR model and subsequently fit the model. When used in conjunction with an existing methodology, specifically Durbin's algorithm, we show that our proposed method can be used as a criterion to optimally fit ARMA models. Empirical results 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.