The time plot of the series NCOP reveals a peak in 2008 and a depression in early 2009. The overall trend is horizontal and no seasonality is obvious. Twelve-month differencing yields SDNCOP exhibiting still a peak in 2008 and a trough in 2009, the overall trend being slightly positive and...

Our starting place is the first order seasonal autoregressive model. Its series are shown to have canonical model-based decompositions whose finite-sample estimates, filters, and error covariances have simple revealing formulas from basic linear regression.We obtain analogous formulas for...