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Periodic linear-quadratic methods for modeling seasonality

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Author Info
Richard M. Todd
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.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 127.

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Date of creation: 1989
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Publication status: Published in Journal of Economic Dynamics and Control (Vol. 14, n. 3-4, July/Oct 1990, pp.763-795)
Handle: RePEc:fip:fedmsr:127

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Keywords: Seasonal variations (Economics);

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  3. Parzen, Emanuel & Pagano, Marcello, 1979. "An approach to modeling seasonally stationary time series," Journal of Econometrics, Elsevier, vol. 9(1-2), pages 137-153, January. [Downloadable!] (restricted)
  4. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis. [Downloadable!]
  5. Ghysels, Eric, 1987. "Seasonal Extraction in the Presence of Feedback," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(2), pages 191-94, April.
  6. Mark Gersovitz & James G. MacKinnon, 1977. "Seasonality in Regression: An Application of Smoothness Priors," Working Papers 257, Queen's University, Department of Economics. [Downloadable!]
  7. Eichenbaum, Martin S., 1984. "Rational expectations and the smoothing properties of inventories of finished goods," Journal of Monetary Economics, Elsevier, vol. 14(1), pages 71-96, July. [Downloadable!] (restricted)
  8. Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June. [Downloadable!] (restricted)
  9. Ghysels, E., 1986. "A Study Towards a Dynamic Theory of Seasonality for Economic Time Series," Cahiers de recherche 8612, Universite de Montreal, Departement de sciences economiques.
  10. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May. [Downloadable!] (restricted)
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  11. Kenneth F. Wallis, 1978. "Seasonal Adjustment and Multiple Time Series Analysis," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 347-364 National Bureau of Economic Research, Inc. [Downloadable!]
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  12. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
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  13. Lars Peter Hansen & Thomas J. Sargent, 1990. "Recursive Linear Models of Dynamic Economies," NBER Working Papers 3479, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  14. Manuelli, Rodolfo & Sargent, Thomas J., 1988. "Models of business cycles : A review essay," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 523-542. [Downloadable!] (restricted)
  15. Osborn, Denise R & Smith, Jeremy P, 1989. "The Performance of Periodic Autoregressive Models in Forecasting Seasonal U. K. Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 117-27, January.
  16. Eckstein, Zvi, 1984. "A Rational Expectations Model of Agricultural Supply," Journal of Political Economy, University of Chicago Press, vol. 92(1), pages 1-19, February. [Downloadable!] (restricted)
  17. Sargent, Thomas J, 1978. "Estimation of Dynamic Labor Demand Schedules under Rational Expectations," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 1009-44, December. [Downloadable!] (restricted)
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  18. Osborn, Denise R, 1988. "Seasonality and Habit Persistence in a Life Cycle Model of Consumptio n," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 255-66, October-D. [Downloadable!] (restricted)
  19. Singleton, Kenneth J., 1988. "Econometric issues in the analysis of equilibrium business cycle models," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 361-386. [Downloadable!] (restricted)
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