  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.
