IDEAS home Printed from https://ideas.repec.org/p/fip/fedmsr/127.html
   My bibliography  Save this paper

Periodic linear-quadratic methods for modeling seasonality

Author

Listed:
  • 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.

Suggested Citation

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

    Download full text from publisher

    File URL: http://minneapolisfed.org/research/sr/sr127.pdf
    Download Restriction: no
    File URL: http://minneapolisfed.org/research/common/pub_detail.cfm?pb_autonum_id=408
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-681, September.
    2. 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.
    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.
    4. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
    5. 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.
    6. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    7. 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.
    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.
    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. Lars Peter Hansen & Thomas J. Sargent, 1993. "Recursive linear models of dynamic economies," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    11. 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.
    12. Mark Gersovitz & James G. MacKinnon, 1977. "Seasonality in Regression: An Application of Smoothness Priors," Working Paper 257, Economics Department, Queen's University.
    13. Arulampalam, W. & Robin A. Naylor & Jeremy P. Smith, 2002. "University of Warwick," Royal Economic Society Annual Conference 2002 9, Royal Economic Society.
    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.
    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 117-127, 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.
    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 1009-1044, December.
    18. 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.
    19. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ghysels, E., 1992. "Charistmas, Spring and the Dawning of Economic Recovery," Cahiers de recherche 9215, Universite de Montreal, Departement de sciences economiques.
    2. Ghysels, E., 1993. "A Time Series Model with Periodic Stochastic Regime Switching," Cahiers de recherche 9314, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Christiano, Lawrence J. & Todd, Richard M., 2002. "The conventional treatment of seasonality in business cycle analysis: does it create distortions?," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 335-364, March.
    4. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    5. Lars Peter Hansen & Thomas J. Sargent, 1993. "Recursive linear models of dynamic economies," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    6. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    7. Jeffrey A. Miron, 1996. "The Economics of Seasonal Cycles," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262133237, December.
    8. John B. Taylor, 1983. "Rational Expectations Models in Macroeconomics," NBER Working Papers 1224, National Bureau of Economic Research, Inc.
    9. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.
    10. Franses, Ph.H.B.F. & Paap, R., 1999. "Forecasting with periodic autoregressive time series models," Econometric Institute Research Papers EI 9927-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Łukasz Lenart, 2017. "Examination of Seasonal Volatility in HICP for Baltic Region Countries: Non-Parametric Test versus Forecasting Experiment," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(1), pages 29-67, March.
    12. Fabrice Collard & Patrick Fève, 2012. "Sur les causes et les effets en macro économie : les Contributions de Sargent et Sims, Prix Nobel d'Economie 2011," Revue d'économie politique, Dalloz, vol. 122(3), pages 335-364.
    13. Yorghos Tripodis & Jeremy Penzer, 2009. "Modelling time series with season-dependent autocorrelation structure," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(7), pages 559-574.
    14. Matthew D. Shapiro, 1986. "The Dynamic Demand for Capital and Labor," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(3), pages 513-542.
    15. Eichenbaum, Martin, 1989. "Some Empirical Evidence on the Production Level and Production Cost Smoothing Models of Inventory Investment," American Economic Review, American Economic Association, vol. 79(4), pages 853-864, September.
    16. Langley, Suchada Vichitakul, 1982. "The formation of price expectations: a case study of the soybean market," ISU General Staff Papers 198201010800009358, Iowa State University, Department of Economics.
    17. 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.
    18. Tinsley, P A, 2002. "Rational Error Correction," Computational Economics, Springer;Society for Computational Economics, vol. 19(2), pages 197-225, April.
    19. Tim Bollerslev & Eric Ghysels, 1994. "On Periodic Autogressive Conditional Heteroskedasticity," CIRANO Working Papers 94s-03, CIRANO.
    20. Braun, R. Anton & Evans, Charles L., 1995. "Seasonality and equilibrium business cycle theories," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 503-531, April.

    More about this item

    Keywords

    Seasonal variations (Economics);

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedmsr:127. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Jannelle Ruswick (email available below). General contact details of provider: https://edirc.repec.org/data/cfrbmus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.