Periodic Linear-Quadratic Methods for Modeling Seasonality

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Optimal linear regulator methods are used to represent a class of models of endogenous equilibrium seasonality that has so far received little attention. Seasonal structure is built into these models in either of two equivalent ways: periodically varying the coefficient matrices of a formerly nonseasonal problem or embedding this periodic-coefficient problem in a higher-dimensional sparse system whose time-invariant matrices have a special pattern of zero blocks. The former structure is compact and convenient computationally; the latter can be used to apply familiar convergence results from the theory of time-invariant optimal regulator problems. The new class of seasonality models provides an equilibrium interpretation for empirical work involving periodically stationary time series.

Published in: Journal of Economic Dynamics and Control (Vol 14, No. 3-4, July - Oct 1990, pp. 763-795) https://doi.org/10.1016/0165-1889(90)90042-F.