The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Seasonal Adjustment

  • Svend Hylleberg
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2408

Abstract

The main objective of seasonally adjusted time series is to provide easy access to a common time series data-set purged of what is considered seasonal noise. Although the application of officially seasonally adjusted data may save costs, it may also imply less efficient use of the information available, and data may be distorted. Hence, in many cases, seasonality may need to be treated as an integrated part of an econometric analysis. In this article we present several ways to integrate seasonal adjustment into econometric analysis in addition to applying data adjusted by the two most popular adjustment methods.

Keywords

ARIMA models ARMA models Autoregressive models Band spectrum regression Band-pass filters Basic structural model (BSM) Box–Jenkins model Cointegration Common seasonal features Evolving seasonals model Habit persistence HEGY test Henderson moving averages Jevons, W. Kalman filter Long memory Maximum likelihood Noise models Ordinary least squares (OLS) Periodic autoregressive model (PAR) Periodic cointegration Production smoothing Real business cycles Seasonal adjustment Seasonal cointegration Seasonal difference filter Seasonal dummies Time series models TRAMO/SEATS seasonal adjustment programme Transformations Univariate seasonal models Unobserved components (UC) models Vector autoregressions X-11 seasonal adjustment programme 

JEL Classifications

C1 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgment

The author is grateful for helpful comments from Niels Haldrup and Steven Durlauf.

Bibliography

  1. Arteche, J. 2000. Gaussian semiparametric estimation in seasonal/cyclical long memory time series. Kybernetika 36: 279–310.Google Scholar
  2. Arteche, J., and P. Robinson. 2000. Semiparametric inference in seasonal and cyclical long memory processes. Journal of Time Series Analysis 21: 1–25.CrossRefGoogle Scholar
  3. Baxter, M., and R. King. 1999. Measuring business cycles: Approximate band-pass filters for economic time series. Review of Economics and Statistics 81: 575–593.CrossRefGoogle Scholar
  4. Beaulieu, J., and J. Miron. 1993. Seasonal unit roots in aggregate US data. Journal of Econometrics 55: 305–328.CrossRefGoogle Scholar
  5. Birchenhal, C., R. Bladen-Howell, A. Chui, D. Osborn, and J. Smith. 1989. A seasonal model of consumption. Economic Journal 99: 837–843.CrossRefGoogle Scholar
  6. Boswijk, H., and P. Franses. 1995. Periodic cointegration: Representation and inference. Review of Economics and Statistics 77: 436–454.CrossRefGoogle Scholar
  7. Box, G., and G. Jenkins. 1970. Time series analysis, forecasting, and control. San Francisco: Holden-Day.Google Scholar
  8. Braun, R., and C. Evans. 1995. Seasonality and equilibrium business cycle theories. Journal of Economic Dynamics and Control 19: 503–531.CrossRefGoogle Scholar
  9. Brendstrup, B., S. Hylleberg, M. Nielsen, L. Skipper, and L. Stentoft. 2004. Seasonality in economic models. Macroeconomic Dynamics 8: 362–394.CrossRefGoogle Scholar
  10. Brillinger, D. 1981. Time series: Data analysis and theory. San Francisco: Holden Day.Google Scholar
  11. Bunzel, H., and 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.CrossRefGoogle Scholar
  12. Busetti, F., and A. Harvey. 2003. Seasonality tests. Journal of Business and Economic Statistics 21: 421–436.Google Scholar
  13. Canova, F., and 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
  14. Chatterjee, S., and B. Ravikumar. 1992. A neoclassical model of seasonal fluctuations. Journal of Monetary Economics 29: 59–86.CrossRefGoogle Scholar
  15. Cubadda, G. 1999. Common cycles in seasonal non-stationary time series. Journal of Applied Econometrics 14: 273–291.CrossRefGoogle Scholar
  16. Cubadda, G. 2001. Complex reduced rank models for seasonally cointegrated time series. Oxford Bulletin of Economics and Statistics 63: 497–511.CrossRefGoogle Scholar
  17. Cubadda, G., G. Savio, and R. Zelli. 2002. Seasonality, productivity shocks, and sectoral comovements in a real business cycle model for Italy. Macroeconomic Dynamics 6: 337–356.CrossRefGoogle Scholar
  18. Dagum, E. 1980. The X-11-ARIMA seasonally adjustment method. Technical Report 12–564E. Ottawa: Statistics Canada.Google Scholar
  19. Dickey, D., and W. 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
  20. Dickey, D., D. Hasza, and W. Fuller. 1984. Testing for unit roots in seasonal time series. Journal of the American Statistical Association 79: 355–367.CrossRefGoogle Scholar
  21. Engle, R. 1974. Band spectrum regression. International Economic Review 15: 1–11.CrossRefGoogle Scholar
  22. Engle, R. 1978. Estimating structural models of seasonality. In Seasonal analysis of economic time series, ed. A. Zellner. Washington, DC: US Census Bureau.Google Scholar
  23. Engle, R. 1980. Exact maximum likelihood methods for dynamic regressions and band spectrum regressions. International Economic Review 21: 391–407.CrossRefGoogle Scholar
  24. Engle, R., and C. Granger. 1987. Co-integration and error correction: Representation, estimation and testing. Econometrica 55: 251–276.CrossRefGoogle Scholar
  25. Engle, R., C. Granger, and 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.CrossRefGoogle Scholar
  26. Engle, R., C. Granger, S. Hylleberg, and H. Lee. 1993. Seasonal cointegration – the Japanese consumption function. Journal of Econometrics 55: 275–298.CrossRefGoogle Scholar
  27. Engle, R., and S. Hylleberg. 1996. Common seasonal features: Global unemployment. Oxford Bulletin of Economics and Statistics 58: 615–630.CrossRefGoogle Scholar
  28. Engle, R., and S. Kozicki. 1993. Testing for common features. Journal of Business and Economic Statistics 11: 369–380.Google Scholar
  29. Findley, D., B. Monsell, W. Bell, M. Otto, and B. 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
  30. Franses, P. 1996. Periodicity and Stochastic trends in economic time series. Oxford: Oxford University Press.Google Scholar
  31. Frisch, R., and F. Waugh. 1933. Partial time regressions as compared with individual trends. Econometrica 1: 387–401.CrossRefGoogle Scholar
  32. Fuller, W. 1976. Introduction to statistical time series. New York: John Wiley and Sons.Google Scholar
  33. Gersovitz, M., and J. MacKinnon. 1978. Seasonality in regression: An application of smoothness priors. Journal of the American Statistical Association 73: 264–273.CrossRefGoogle Scholar
  34. Ghysels, E. 1988. A study towards a dynamic theory of seasonality for economics time series. Journal of the American Statistical Association 83: 68–72.CrossRefGoogle Scholar
  35. Ghysels, E. 1997. Seasonal adjustments and other data transformations. Journal of Business and Economic Statistics 15: 410–418.Google Scholar
  36. Ghysels, E., and D. Osborn. 2001. The econometric analysis of seasonal time series. Cambridge, MA: Cambridge University Press.CrossRefGoogle Scholar
  37. Gil-Alana, L., and P. Robinson. 1997. Testing of unit root and other non-stationary hypotheses in macroeconomic time series. Journal of Econometrics 80: 241–268.CrossRefGoogle Scholar
  38. Gomez, V., and A. Maravall. 1996. Programs TRAMO and SEATS. Madrid: Banco de Espana.Google Scholar
  39. Haldrup, N., S. Hylleberg, G. Pons, and A. Sanso. 2007. Common periodic correlation features and the interaction of stocks and flows in daily airport data. Journal of Business and Economic Statistics 25: 21–32.CrossRefGoogle Scholar
  40. Hannan, E. 1960. Time series analysis. London: Methuen.Google Scholar
  41. Hannan, E., R. Terrell, and N. Tuckwell. 1970. The seasonal adjustment of economic time series. International Economic Review 11: 24–52.CrossRefGoogle Scholar
  42. Harvey, A. 1993. Time series models. London: Prentice Hall/Harvester Wheatsheaf.Google Scholar
  43. Harvey, A., and A. Scott. 1994. Seasonality in dynamic regression models. Economic Journal 104: 1324–1345.CrossRefGoogle Scholar
  44. Harvey, A., S. Koopman, and N. Shephard, ed. 2004. State space and unobserved component models: theory and applications. Cambridge, MA: Cambridge University Press.Google Scholar
  45. Hood, C., J. Ashley, and D. Findley. 2004. An empirical evaluation of the performance of TRAMo/SEATS on simulated series. Technical report. Washington, DC: US Census Bureau.Google Scholar
  46. Hylleberg, S. 1977. A comparative study of finite sample properties of band spectrum regression estimators. Journal of Econometrics 5: 167–182.CrossRefGoogle Scholar
  47. Hylleberg, S. 1986. Seasonality in Regression. Orlando: Academic Press.Google Scholar
  48. Hylleberg, S., ed. 1992. Modelling seasonality. Oxford: Oxford University Press.Google Scholar
  49. Hylleberg, S. 1995. Tests for seasonal unit roots: General to specific or specific to general. Journal of Econometrics 69: 5–25.CrossRefGoogle Scholar
  50. Hylleberg, S., R. Engle, C. Granger, and S. Yoo. 1990. Seasonal integration and cointegration. Journal of Econometrics 44: 215–238.CrossRefGoogle Scholar
  51. Hylleberg, S., and A. Pagan. 1997. Seasonal integration and the evolving seasonals model. International Journal of Forecasting 13: 329–340.CrossRefGoogle Scholar
  52. Jevons, W. 1884. Investigations in currency and finances. London: Macmillan.Google Scholar
  53. Johansen, S. 1995. Likelihood-based inference in cointegrated vector autoregressive models. Oxford: Oxford University Press.CrossRefGoogle Scholar
  54. Johansen, S., and E. Schaumburg. 1999. Likelihood analysis of seasonal cointegration. Journal of Econometrics 88: 301–339.CrossRefGoogle Scholar
  55. Koop, G., and H. Dijk. 2000. Testing for integration using evolving trend and seasonals models: A Bayesian approach. Journal of Econometrics 97: 261–291.CrossRefGoogle Scholar
  56. Kunst, R. 1997. Testing for cyclical non-stationarity in autoregressive processes. Journal of Time Series Analysis 18: 123–135.CrossRefGoogle Scholar
  57. Kwiatkowski, D., P. Phillips, P. Schmidt, and 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.CrossRefGoogle Scholar
  58. Lee, H. 1992. Maximum likelihood inference on cointegration and seasonal cointegration. Journal of Econometrics 54: 1–47.CrossRefGoogle Scholar
  59. Lovell, M. 1963. Seasonal adjustment of economic time series. Journal of the American Statistical Association 58: 993–1010.CrossRefGoogle Scholar
  60. Mazzi, G.L., and G. Savio. 2005. The seasonal adjustment of short time series. Technical Report KS-DT-05-002. EUROSTAT.Google Scholar
  61. Mills, F. 1924. Statistical methods. London: Pitman.Google Scholar
  62. Miron, J. 1996. The economics of seasonal cycles. Cambridge, MA: MIT Press.Google Scholar
  63. Miron, J., and S. Zeldes. 1988. Seasonality, cost shocks and the production smoothing model of inventories. Econometrica 56: 877–908.CrossRefGoogle Scholar
  64. OECD. 1999. Feature article: Seasonal adjustment. Main Economic Indicators. November. Paris: OECD.Google Scholar
  65. Osborn, D. 1988. Seasonality and habit persistence in a life cycle model of consumption. Journal of Applied Econometrics 3: 255–266.CrossRefGoogle Scholar
  66. Osborn, D. 1991. The implications of periodically varying coefficients for seasonal time-series processes. Journal of Econometrics 48: 373–384.CrossRefGoogle Scholar
  67. Shiskin, J., A. Young, and J. Musgrave. 1967. The X-11 variant of the census method II seasonal adjustment program. Technical Paper No. 15. Washington, DC: US Census Bureau.Google Scholar
  68. Taylor, A. 2005. Variance ratio tests of the seasonal unit root hypothesis. Journal of Econometrics 124: 33–54.CrossRefGoogle Scholar
  69. Vahid, F., and R. Engle. 1993. Common trends and common cycles. Journal of Applied Econometrics 8: 341–360.Google Scholar
  70. Wallis, K. 1998. Comment. Journal of Business and Economic Statistics 16: 164–165.Google Scholar
  71. Wells, J. 1997. Business cycles, seasonal cycles, and common trends. Journal of Macroeconomics 19: 443–469.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Svend Hylleberg
    • 1
  1. 1.