Jan Willems has introduced an alternative methodology for time series which is not based on statistics, but on direct analysis. It seems likely that this will be a superior approach to conventional. The reasons is that the basic assumptions for statistical times series analysis are NOT plausible. Why should the errors by i.i.d.? Why should the series be stationary? Why is it plausible to model them as draws from random distribution? The answers to all these questions are not in favor of statistical analysis. One paper which introduces the basic ideas of Willems is:
From Time Series to Linear System -- Part I: Finite Dimensional Linear Time Invariant Systems.
Automatica, Vol 22, No. 5, pages 561-580