Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-02T18:45:27.427Z Has data issue: false hasContentIssue false
  • English
  • Français

SEASONALITY IN ECONOMIC MODELS

Published online by Cambridge University Press:  10 June 2004

BJARNE BRENDSTRUP ,
SVEND HYLLEBERG ,
MORTEN ØRREGAARD NIELSEN ,
LARS SKIPPER  and
LARS STENTOFT
BJARNE BRENDSTRUP
Affiliation:
University of Aarhus
SVEND HYLLEBERG
Affiliation:
University of Aarhus
MORTEN ØRREGAARD NIELSEN
Affiliation:
University of Aarhus
LARS SKIPPER
Affiliation:
University of Aarhus
LARS STENTOFT
Affiliation:
University of Aarhus
Get access Rights & Permissions [Opens in a new window]

Abstract

Seasonality has been a major research area in economics for several decades. The paper assesses the recent development in the literature on the treatment of seasonality in economics, and divides it into three interrelated groups. The first group, pure noise models, consists of methods based on the view that seasonality is noise contaminating the data or, more correctly, contaminating the information of interest for the economists. The second group, time-series models, treats seasonality as a more integrated part of the modeling strategy, with the choice of model being data driven. The third group, economic models of seasonality, introduces economic theory, that is, optimizing behavior, into the modeling of seasonality.

Keywords

SeasonalityEconomic Models
Type
MD SURVEY
Information
Macroeconomic Dynamics , Volume 8 , Issue 3 , June 2004 , pp. 362 - 394
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Almon S. 1965 The distributed lag between capital appropriations and expenditures. Econometrica 33, 178 196.Google Scholar
Arteche J. 2000 Gaussian semiparametric estimation in seasonal/cyclical long memory time series. Kybernetika 36, 279– 310.Google Scholar
Arteche J. & P.M. Robinson 2000 Semiparametric inference in seasonal and cyclical long memory processes. Journal of Time Series Analysis 21, 1– 25.Google Scholar
Baillie R.T. 1996 Long memory processes and fractional integration in econometrics. Journal of Econometrics 73, 5– 59.Google Scholar
Baxter M. & R.G. King 1999 Measuring business cycles: Approximate band-pass filters for economic time series. Review of Economics and Statistics 81, 575– 593.Google Scholar
Beaulieu J.K. & J.A. Miron 1992a Why do countries and industries with large seasonal cycles also have large business cycles? Quarterly Journal of Economics 107, 621– 656.Google Scholar
Beaulieu J.J. & J.A. Miron 1992b A cross country comparison of seasonal cycles and business cycles. Economic Journal 102, 772– 788.Google Scholar
Beaulieu J.J. & J.A. Miron 1993 Seasonal unit roots in aggregate US data. Journal of Econometrics 55, 305– 328.Google Scholar
Beran J. 1994 Statistics for Long-Memory Processes. New York: Chapman-Hall.
Birchenhal C.R., R.C. Bladen-Howell, A.P.L. Chui, D.R. Osborn & J.P. Smith 1989 A seasonal model of consumption. Economic Journal 99, 837– 843.Google Scholar
Boswijk H.P. & P.H. Franses 1995 Periodic cointegration: Representation and inference. Review of Economics and Statistics 77, 436– 454.Google Scholar
Box G.E.P. & G.M. Jenkins 1970 Time Series Analysis, Forecasting, and Control. San Francisco: Holden-Day.
Braun R.A. & C.L. Evans 1995 Seasonality and equilibrium business cycle theories. Journal of Economic Dynamics and Control 19, 503– 531.Google Scholar
Breitung J. 2002 Nonparametric tests for unit roots and cointegration. Journal of Econometrics 108, 343– 363.Google Scholar
Breitung J. & P.H. Franses 1998 On the Phillips-Perron type tests for seasonal unit roots. Econometric Theory 14, 200– 221.Google Scholar
Brillinger D.R. 1981 Time Series: Data Analysis and Theory. San Francisco: Holden-Day.
Bunzel H. & S. Hylleberg 1982 Seasonality in dynamic regression models: A comparative study of finite sample properties of various regression estimators including band spectrum regression. Journal of Econometrics 19, 345– 366.Google Scholar
Burridge P. & A.M.R. Taylor 2001 On the properties of regression based test for seasonal unit roots in the presence of higher order serial correlation. Journal of Business and Economic Statistics 19, 374– 379.Google Scholar
Caner M. 1998 A locally optimal seasonal unit-root test. Journal of Business and Economic Statistics 16, 349– 356.Google Scholar
Canova F. & B. Hansen 1995 Are seasonal patterns constant over time? A test for seasonal stability. Journal of Business and Economic Statistics 13, 237– 252.Google Scholar
Cecchetti S.G. & A.K. Kashyap 1996 International cycles. European Economic Review 40, 331– 360.Google Scholar
Cecchetti S.G., A.K. Kashyap & D.W. Wilcox 1997 Interactions between the seasonal and business cycles in production and inventories. American Economic Review 87, 884– 892.Google Scholar
Chatterjee S. & B. Ravikumar 1992 A neoclassical model of seasonal fluctuations. Journal of Monetary Economics 29, 59– 86.Google Scholar
Christiano L. & R.M. Todd 2002 The conventional treament of seasonality in business cycle analysis: Does it create distortions? Journal of Monetary Economics 49, 335– 364.Google Scholar
Cubadda G. 1999 Common cycles in seasonal non-stationary time series. Journal of Applied Econometrics 14, 273– 291.Google Scholar
Cubadda G. 2001 Complex reduced rank models for seasonally cointegrated time series. Oxford Bulletin of Economics and Statistics 63, 497– 511.Google Scholar
Cubadda G.,G. Savio & R. Zelli 2002 Seasonality, productivity shocks, and sectoral comovements in a real business cycle model for Italy. Macroeconomic Dynamics 6, 337– 356.Google Scholar
Dahlhaus R. 1989 Efficient parameter estimation for self-similar processes. Annals of Statistics 17, 1749– 1766.Google Scholar
Dickey D.A. & W.A. Fuller 1979 Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427– 431.Google Scholar
Dickey D.A., D.P. Hasza & W.A. Fuller 1984 Testing for unit roots in seasonal time series. Journal of the American Statistical Association 79, 355– 367.Google Scholar
Engle R.F. 1974 Band spectrum regression. International Economic Review 15, 1– 11.Google Scholar
Engle R.F. 1978 Estimating structural models of seasonality. In A. Zellner (ed.), Seasonal Analysis of Economic Time Series, pp. 281– 297. Washington, DC: U.S. Department of Commerce, Bureau of the Census.
Engle R.F. 1980 Exact maximum likelihood methods for dynamic regressions and band spectrum regressions. International Economic Review 21, 391– 407.Google Scholar
Engle R.F. & C.W.J. Granger 1987 Co-integration and error correction: Representation, estimation and testing. Econometrica 55, 251– 276.Google Scholar
Engle R.F. & S. Hylleberg 1996 Common seasonal features: Global unemployment. Oxford Bulletin of Economics and Statistics 58, 615– 630.Google Scholar
Engle R.F. & S. Kozicki 1993 Testing for common features. Journal of Business and Economic Statistics 11, 369– 380.Google Scholar
Engle R.F., C.W.J. Granger & J. Hallman 1989 Merging short and long run forecasts: An application of seasonal cointegration to monthly electricity sales forecasting. Journal of Econometrics 40, 45– 62.Google Scholar
Engle R.F., C.W.J. Granger, S. Hylleberg & H.S. Lee 1993 Seasonal cointegration—The Japanese consumption function. Journal of Econometrics 55, 275– 298.Google Scholar
Findley D.F., B.C. Monsell W.R. Bell M.C. Otto & B.C. Chen 1998 New capabilities and methods of the X-12-ARIMA seasonal adjustment program. Journal of Business and Economic Statistics 16, 127– 176.Google Scholar
Fox R. & M.S. Taqqu 1986 Large-sample properties of parameter estimates for strongly dependent stationary Gaussian series. Annals of Statistics 14, 517– 532.Google Scholar
Franses P.H. 1991 Seasonality, nonstationarity and the forecasting of monthly time series. International Journal of Forecasting 7, 199– 208.Google Scholar
Franses P.H. 1993 A method to select between periodic cointegration and seasonal cointegration. Economics Letters 63, 7– 10.Google Scholar
Franses P.H. 1996 Periodicity and Stochastic Trends in Economic Time Series. Oxford: Oxford University Press.
Franses P.H. & T. Kloek 1995 A periodic cointegration model of quarterly consumption. Applied Stochastic Models and Data Analysis 11, 159– 166.Google Scholar
Franses P.H. & T. Vogelsang 1998 On seasonal cycles, unit roots, and mean shifts. Review of Economics and Statistics 80, 231– 240.Google Scholar
Frisch R. & F.V. Waugh 1933 Partial time regressions as compared with individual trends. Econometrica 1, 387– 401.Google Scholar
Fuller W.A. 1976 Introduction to Statistical Time Series, New York: John Wiley and Sons.
Gersovitz M. & J.G. MacKinnon 1978 Seasonality in regression: An application of smoothness priors. Journal of the American Statistical Association 73, 264– 273.Google Scholar
Geweke J. & S. Porter-Hudak 1983 The estimation and application of long memory time series models. Journal of Time Series Analysis 4, 221– 238.Google Scholar
Ghysels E. 1988 A study towards a dynamic theory of seasonality for economics time series. Journal of the American Statistical Association 83, 68– 72.Google Scholar
Ghysels E. & D.R. Osborn 2001 The Econometric Analysis of Seasonal Time Series. Cambridge: Cambridge University Press.
Ghysels E., H.S. Lee & J. Noh 1994 Testing for unit roots in seasonal time series. Some theoretical extensions and a Monte Carlo investigation. Journal of Econometrics 62, 415– 442.Google Scholar
Ghysels E., A. Hall & H.S. Lee 1996 On periodic structures and testing for seasonal unit roots. Journal of the American Statistical Association 91, 1551– 1559.Google Scholar
Gil-Alana L.A. & P.M. Robinson 1997 Testing of unit root and other non-stationary hypotheses in macroeconomic time series. Journal of Econometrics 80, 241– 268.Google Scholar
Gomez V. & A. Maravall 1996 Programs TRAMO and SEATS, Banco de Espana.
Granger C.W.J. 1981 Some properties of time series data and their use in econometric model specification. Journal of Econometrics 16, 121– 130.Google Scholar
Granger C.W.J. & R. Joyeux 1980 An introduction to long memory time series models and fractional differencing. Journal of Time Series Analysis 1, 15– 39.Google Scholar
Granger C.W.J. & M. Morris 1976 Time series modelling and interpretation. Journal of the Royal Statistical Society Series A 38, 248– 257.Google Scholar
Haldrup N., A. Montanes & A. Sanso 2000 Measurement Errors and Outliers in seasonal Unit Root Testing. Working paper, University of Aarhus.
Hall R.E. 1978 Stochastic implications of the life cycle-permanent income hypothesis: Theory and evidence. Journal of Political Economy 86, 971– 986.Google Scholar
Hannan E.J. 1960 Time Series Analysis. London: Methuen.
Hannan E.J., R.D. Terrell & N.E. Tuckwell 1970 The seasonal adjustment of economic time series. International Economic Review 11, 24– 52.Google Scholar
Hansen L.P. & T.J. Sargent 2000 Wanting Robustness in Macroeconomics. Working paper, University of Chicago.
Harvey A.C. 1993 Time Series Models. Cambridge, MA: MIT Press.
Harvey A.C. & A. Scott 1994 Seasonality in dynamic regression models. Economic Journal 104, 1324– 1345.Google Scholar
Hassler U. & P.M.M. Rodrigues 2003 Seasonal unit root tests under structural breaks. Journal of Time Series Analysis.Google Scholar
Hodrick R.J. & E.C. Prescott 1980 Post-War U.S. Business Cycles: An Empirical Investigation. Working paper, Carnegie-Mellon University.
Hosking J.R.M. 1981 Fractional differencing. Biometrika 68, 165– 176.Google Scholar
Hylleberg S. 1977 A comparative study of finite sample properties of band spectrum regression estimators. Journal of Econometrics 5, 167– 182.Google Scholar
Hylleberg S. 1986 Seasonality in Regression. Orlando, FL: Academic Press.
Hylleberg S. 1992 Modelling Seasonality. Oxford: Oxford University Press.
Hylleberg S. 1995 Tests for seasonal unit roots. General to specific or specific to general. Journal of Econometrics 69, 5– 25.Google Scholar
Hylleberg S. & A.R. Pagan 1997 Seasonal integration and the evolving seasonals model. International Journal of Forecasting 13, 329– 340.Google Scholar
Hylleberg S., R.F. Engle, C.W.J. Granger & S. Yoo 1990 Seasonal integration and cointegration. Journal of Econometrics 44, 215– 238.Google Scholar
Hylleberg S., C. Jørgensen & N.K. Sørensen 1993 Seasonality in macroeconomic time series. Empirical Economics 18, 321– 335.Google Scholar
Jevons W.S. 1862/1884 On the Study of Periodic Commercial Fluctuations, pp. 2– 11. 1884 edn. London: Macmillan.
Johansen S. 1995 Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford, UK: Oxford University Press.
Johansen S. & E. Schaumburg 1999 Likelihood analysis of seasonal cointegration. Journal of Econometrics 88, 301– 339.Google Scholar
Judd K. 1998 Numerical Methods in Economics. Cambridge, MA: MIT Press.
Koop G. & H.K.V. Dijk 2000 Testing for integration using evolving trend and seasonals models: A Bayesian approach. Journal of Econometrics 97, 261– 291.Google Scholar
Künsch H.R. 1987 Statistical aspects of self-similar processes. In Y. Prokhorov & V.V. Sazanov (eds.), Proceedings of the First World Congress of the Bernoulli Society, pp. 67– 74. Utrecht: VNU Science Press.
Kunst R. & M. Reutter 2002 Decisions on seasonal unit roots. Journal of Statistical Computation and Simulation 72, 403– 418.Google Scholar
Kwiatkowski D., P.C.B. Phillips, P. Schmidt & Y. Shin 1992 Testing the null hypothesis of stationarity against the alternative of a unit root—how sure are we that economic time series have a unit root? Journal of Econometrics 54, 159– 178.Google Scholar
Kydland F. & E.C. Prescott 1990 Real facts and a monetary myth. FRBM: Quaterly Review 14, 3– 18.Google Scholar
Lee H.S. 1992 Maximum likelihood inference on cointegration and seasonal cointegration. Journal of Econometrics 54, 1– 47.Google Scholar
Lildholdt P. 2001 Long Memory at the Seasonal Frequencies—Due to Aggregation. Mimeo, University of Aarhus.
Lovell M.C. 1963 Seasonal adjustment of economic time series. Journal of the American Statistical Association 58, 993– 1010.Google Scholar
Miron J.A. 1996 The Economics of Seasonal Cycles. Cambridge, MA: MIT Press.
Miron J.A. & S.P. Zeldes 1988 Seasonality, cost shocks and the production smoothing model of inventories. Econometrica 56, 877– 908.Google Scholar
Nielsen M.Ø. 2003 Efficient likelihood inference in nonstationary univariate models. Econometric Theory 20, 116– 146.Google Scholar
Osborn D.R. 1988 Seasonality and habit persistence in a life cycle model of consumption. Journal of Applied Econometrics 3, 255– 266.Google Scholar
Osborn D.R. 1991 The implications of periodically varying coefficients for seasonal time-series processes. Journal of Econometrics 48, 373– 384.Google Scholar
Osborn D.R. 2000 Cointegration for seasonal time series processes. Working paper, University of Manchester.
Osterwald-Lenum M. 1992 Recalculated and extended tables of the asymptotic distribution of some important maximum likelihood cointegration test statistics. Bulletin of Economics and Statistics 54, 461– 472.Google Scholar
Plosser C.I. 1978 A time series analysis of seasonality in econometric models. In A. Zellner (ed.), Seasonal Analysis of Economic Time Series, pp. 365– 393. Washington, DC: U.S. Department of Commerce, Bureau of the Census.
Porter-Hudak S. 1990 An application of the seasonal fractionally differenced model to the monetary aggregates. Journal of the American Statistical Association 85, 338– 344.Google Scholar
Prescott E.C. 1986 Theory ahead of business cycle measurement. Carnegie-Rochester Conference Series on Public Policy 25, 11– 66.Google Scholar
Proietti T. 1998 Spurious periodic autoregressions. Econometrics Journal 1, 1– 22.Google Scholar
Robinson P.M. 1994a Efficient tests of nonstationary hypotheses. Journal of the American Statistical Association 89, 1420– 1437.Google Scholar
Robinson P.M. 1994b Time series with strong dependence. In C.A. Sims (ed.), Advances in Econometrics, pp. 47– 95. Cambridge, UK: Cambridge University Press.
Robinson P.M. 1995a Gaussian semiparametric estimation of long range dependence. Annals of Statistics 23, 1630– 1661.Google Scholar
Robinson P.M. 1995b Log-periodogram regression of time series with long range dependence. Annals of Statistics 23, 1048– 1072.Google Scholar
Rodrigues P.M.M. 2002 On LM type tests for seasonal unit roots. Econometrics Journal 5, 176– 195.Google Scholar
Rodrigues P.M.M. & D.R. Osborn 1999 Performance of seasonal unit root tests for monthly data. Journal of Applied Statistics 26, 985– 1004.Google Scholar
Rust J. 1996 Numerical Dynamic Programming in Economics, Ch. . Amsterdam: Elsevier, North-Holland.
Shiskin J., A.H. Young & J.C. Musgrave 1967 The X-11 Variant of the Census Method II Seasonal Adjustment Program. Technical paper 15. Washington, DC: U.S. Department of Commerce, Bureau of Census.
Sims C.A. 1974 Seasonality in regression. Journal of American Statistical Association 69, 618– 627.Google Scholar
Stokey N.L., R.E. Lucas & E.C. Prescott 1989 Recursive Methods in Economic Dynamics, Cambridge: Harvard University Press.
Tam W. & G.C. Reinsel 1997 Tests for seasonal moving average unit root in {ARIMA} models. Journal of the American Statistical Association 92, 725– 738.Google Scholar
Taylor A.M.R. 2002 Variance Ratio Tests of the Seasonal Unit Root Hypothesis. Working paper, University of Birmingham.
Todd R. 1990 Periodic linear-quadratic methods for modeling seasonality. Journal of Economic Dynamics and Control 14, 763– 795.Google Scholar
Vahid F. & R.F. Engle 1993 Common trends and common cycles. Journal of Applied Econometrics 8, 341– 360.Google Scholar
Wallis K.F. 1974 Seasonal adjustment and relations between variables. Journal of the American Statistical Association 69, 18– 31.Google Scholar
Wells J.M. 1997 Business cycles, seasonal cycles, and common trends. Journal of Macroeconomics 19, 443– 469.Google Scholar
Zellner A. (ed.) 1978 Seasonal Analysis of Economic Time Series. Proceedings of the Conference on the Seasonal Analysis of Economic Time Series, Vol. 8. Washington, DC: U.S. Department of Commerce, Bureau of the Census.
Zellner A. (ed.) 1983 Applied Time Series Analysis of Economic Data. Washington DC: US Bureau of the Census.
Zellner A. & F. Palm 1974 Time series analysis and simultaneous equation econometric models. Journal of Econometrics 2, 17– 54.Google Scholar