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Periodic linear-quadratic methods for modeling seasonality

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  • 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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  • Richard M. Todd, 1989. "Periodic linear-quadratic methods for modeling seasonality," Staff Report 127, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:127
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    References listed on IDEAS

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    1. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-681, September.
    2. 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.
    3. Christiano, Lawrence J. & Eichenbaum, Martin, 1987. "Temporal aggregation and structural inference in macroeconomics," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 26(1), pages 63-130, January.
    4. Ghysels, Eric, 1987. "Seasonal Extraction in the Presence of Feedback," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(2), pages 191-194, April.
    5. 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.
    6. 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.
    7. Lars Peter Hansen & Thomas J. Sargent, 1993. "Recursive linear models of dynamic economies," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    8. Arulampalam, W. & Robin A. Naylor & Jeremy P. Smith, 2002. "University of Warwick," Royal Economic Society Annual Conference 2002 9, Royal Economic Society.
    9. Manuelli, Rodolfo & Sargent, Thomas J., 1988. "Models of business cycles : A review essay," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 523-542.
    10. 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 1009-1044, December.
    11. 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.
    12. 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.
    13. 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.
    14. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
    15. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    16. 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.
    17. Mark Gersovitz & James G. MacKinnon, 1977. "Seasonality in Regression: An Application of Smoothness Priors," Working Paper 257, Economics Department, Queen's University.
    18. 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 117-127, January.
    19. 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.
    20. 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 255-266, October-D.
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    Cited by:

    1. Peter A. Zadrozny, 1990. "Estimating A Multivariate Arma Model with Mixed-Frequency Data: An Application to Forecasting U.S. GNP at Monthly Intervals," Working Papers 90-5, Center for Economic Studies, U.S. Census Bureau.

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    Keywords

    Seasonal variations (Economics);

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