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...

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...

We present algorithms for computing the weights implicitly assigned to observations when estimating unobserved components using a model in state space form. The algorithms are for both filtering and signal extraction. In linear time-invariant models such weights can sometimes be obtained...