Seasonal Extraction in the Presence of Feedback

Time series seasonal extraction techniques are quite often applied in the context of a policy aimed at controlling the nonseasonal components of a time series. Monetary policies targeting the nonseasonal components of monetary aggregates are an example. Such policies can be studied as a quadratic optimal control model in which observations are contaminated by seasonal noise. Optimal extraction filters in such models do not correspond to univariate time series seasonal extraction filters. The linear quadratic control model components are nonorthogonal due to the presence of control feedback. This article presents the Kalman filter as a conceptual and computational device used to extract seasonal noise in the presence of feedback.