Report

Periodic linear-quadratic methods for modeling seasonality

Abstract: 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.

https://doi.org/10.21034/sr.127

Bibliographic Information

Provider: Federal Reserve Bank of Minneapolis

Part of Series: Staff Report

Publication Date: 1989

Number: 127