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Periodic Linear-Quadratic Methods for Modeling Seasonality

Staff Report 127 | Published November 1, 1989

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Richard M. Todd Economist
Periodic Linear-Quadratic Methods for Modeling Seasonality


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)