  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.
