Skip to main content
SpringerLink
Log in

A comparison of indicators for evaluating x-11-arima seasonal adjustment

  • Published:
Journal of the Italian Statistical Society Aims and scope Submit manuscript

Summary

The evaluation of the performance of seasonal adjustment procedures is an issue of practical importance in view of the unobservable nature of the components. Looking at just one indicator when judging the overall quality of a procedure may be misleading, even though this is common practice when many series are involved.

The main purpose of this paper is to compare the information content of different synthetic indicators with reference to the X-11-ARIMA procedure.

Sixty-six different types of monthly seasonal series are generated and the seasonal component then extracted by carrying out X-11-ARIMA with standard options. The correlation between the pseudo-true error for each series and various synthetic indicators allows us to compare the latter's reliability, under both the hypotheses of minimum and maximum variance of the pseudo-true seasonal component.

We show that the overall quality indexQ-the indicator most commonly adopted by users of the X-11-ARIMA-is always outperformed by the simpler diagnostics based on the stability of the estimates.

In particular, the “sliding-spans” indicator, proposed by Findley et al. (1990) and included in the diagnostics of the new X-12 procedure, shows a much stronger correlation with the pseudo-true error in the seasonal adjustment.

We also show that the total forecasting errors in the one-year-ahead extrapolation of the seasonal component have a good informative power and perform almost as well as the “sliding-spans” indicator.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bacchilega G. andGambetta, G. (1984).Appunti per un confronto empirico tra diversi metodi di depurazione stagionale, Centro di Specializzazione e Ricerche. Portici, RS 16/84.

    Google Scholar 

  • Bell, W. R. andHillmer, S. C. (1984). Issues Involved with the Seasonal Adjustment of Economic Time Series,Journal of Business and Economic Time Series, 2, 91–349.

    Google Scholar 

  • Box, G. E. P., Hillmer, S. C. andTiao, G. C. (1978). Analysis and Modeling of Seasonal Time Series. InSeasonal Analysis of Economic Time Series, ed. A. Zellner, US Department of Commerce, 320.

  • Box G. E. P. andJenkins, G. M. (1970).Time Series Analysis: Forecasting and Control, San Francisco, Holden-Day.

    MATH  Google Scholar 

  • Burman, J. P. (1967). Assessment of a Seasonal Adjustment Procedure by Spectral Analysis,Statistician, 247–256.

  • Burman, J. P. (1980), Seasonal Adjustment by Signal Extraction, Journal of the Royal Statistical Society, A, 321–37.

  • Burridge, P. andWallis, K. F. (1984). Unobserved-Components Models for Seasonal Adjustment Filters,Journal of Business and Economic Statistics, 2, 350–9.

    Article  Google Scholar 

  • Cleveland, W. P. andTiao, G. C. (1976). Decomposition of Seasonal Time Series: A Model for the Census X-11 Program,Journal of the American Statistical Association, 71, 581–7.

    Article  MATH  MathSciNet  Google Scholar 

  • Dagum, E. B. (1987). Current Issues on Seasonal Adjustment, Working Paper-TSRA 87/6, Statistics Canada, Ottawa.

    Google Scholar 

  • Dagum, E. B. (1988).The X-11-ARIMA/88 Seasonal Adjustment Method, Statistics Canada, Catalogue K1A OT6.

  • Dagum, E. B., Chab, N. andSolomon, B. (1991). The Autocorrelation of Residuals from the X-11-ARIMA Method,Journal of Officials Statistics, 7, 181–194.

    Google Scholar 

  • Engle, R. F. andGranger, C. W. J. (1987). Cointegration on Error Correction: Representation, Estimation and Testing,Econometrica, 55, 251–276.

    Article  MATH  MathSciNet  Google Scholar 

  • Findley, D. F. andMonsell, B. C. (1986). New Techniques for Determining if a Time Series Can Be Seasonally Adjusted Reliably. InRegional Econometric Modelling, eds. M. R. Perryman e G. R. Schimdt, Amsterdam, Kluwer-Nijhoff, 195–228.

    Google Scholar 

  • Findley, D. F., Monsell, B. C., Shulman, H. B. andPugh, M. G. (1990). Sliding-Spans Diagnostics for Seasonal and Related Adjustments,Journal of the American Statistical Association, Vol. 85, N. 410, 345–55.

    Article  Google Scholar 

  • Ghysels, E., Granger, C. W. J. andSiklos, P.L. (1996). Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process?,Journal of the Business and Economic Statistics, Vol. 14, N. 3, 374–86.

    Article  MathSciNet  Google Scholar 

  • Grether, D. M. andNerlove, M. (1970). Some, Properties of “Optimal” Seasonal Adjustment,Econometrica, 38, 682–703.

    Article  Google Scholar 

  • Hylleberg, S. (1996) Comments on Ghysels E., Granger C. W. J. and Siklos P. L. (1996), Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process?,Journal of the Business and Economic Statistics, Vol. 14, N. 3, 388–89.

    Article  Google Scholar 

  • Hillmer, S. C. andTiao, G. C. (1982). An ARIMA-Model-based Approach to Seasonal Adjustment,Journal of American Statistical Association, 77, 63–70.

    Article  MATH  MathSciNet  Google Scholar 

  • Lothian, J. andMorry, M. (1978). A Set of Quality Control Statistics for the X-11-ARIMA Seasonal Adjustment Program, Research Paper, Statistics Canada.

  • Lovell, M. C. (1963). Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis,Journal of the American Statistical Association, 58, 993–1010.

    Article  MATH  MathSciNet  Google Scholar 

  • Maravall, A. (1987). Minimum Mean Squared Error Estimation of the Noise in Unobserved Component Models,Journal of Business and Economic Statistics, 5, 115–120.

    Article  Google Scholar 

  • Maravall, A. andGomez, V. (1992). Signal Extraction in ARIMA Time Series. Program SEATS, European University Working Paper, n. 92/65.

  • Pierce, D. A. (1978). Seasonal Adjustment when both Deterministic and Stochastic Seasonality are Present. InSeasonal Analysis of Economic Time Series, ed. A Zellner, US Department of Commerce, 242.

  • Piccolo, D. (1985). Progetto DESEC: un'esperienza di ricerca statistica sulle serie stagionali,Quadërni di Statistica e econometria, VII, 5–40.

    Google Scholar 

  • Sims, C. A. (1978). Comments on “Seasonality: Causation, Interpretation and Implications” by Clive W. J. Granger. InSeasonal Analysis of Economic Time Series, ed. A. Zellner Washington D.C., US Dept of Commerce, Bureau of the Census.

    Google Scholar 

  • Tukey, J. W. (1978). Comments on “Seasonality: Causation, Interpretation and Implications” by Clive W. J. Granger. InSeasonal Analysis of Economic Time Series, ed. A. Zellner Washington D. C., US Dept of Commerce, Bureau of the Census.

    Google Scholar 

  • Wallis, K. F. (1982). Seasonal Adjustment and Revision of Current Data: Linear Filters for the X-11 Methods,Journal of the Royal Statistical Society, A, 145, 74–85.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Department, Bank of Italy, Italy

    P. Battipaglia

Authors
  1. P. Battipaglia
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Battipaglia, P. A comparison of indicators for evaluating x-11-arima seasonal adjustment. J. It. Statist. Soc. 5, 179–202 (1996). https://doi.org/10.1007/BF02589171

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02589171

Keywords

Search

Navigation