Zusammenfassung
Es werden zwei resistente, d. h. gegen Ausreißer unempfindliche Methoden zur Zerlegung von Zeitreihen vorgestellt. Die erste benutzt gleitende Mediane anstelle der üblichen gleitenden Durchschnitte und vereinfacht das Verfahren SABL. SABL wurde als resistentes Zerlegungspaket kurz nach der Publikation von Tukeys Ideen zur explorativen Datenanalyse entwickelt. Die zweite Methode geht von strukturellen Zeitreihenmodellen aus und verwendet verallgemeinerte glättende Splines, die geeignet robustifiziert werden. Die Resistenzeigenschaften der beiden Verfahren werden anhand des Bruchpunkt-Konzeptes sowie auf der Basis eines Modells diskutiert. Zudem dient das Modell als Grundlage zur Einschätzung ihrer Effizienz.
Abstract
The paper proposes two resistant methods for time series decomposition, i. e., methods that are insensitive to a few aberrant observations. One is based on running medians instead of the usual moving averages and is designed along the lines of SABL, a package developed shortly after Tukey's ideas were published. The other method uses structural time series models and adapts smoothing splines which are suitably robustified. The resistance of the two methods are studied by employing the concept of the breakdown point. Also resistance and efficiency are investigated by the means of a suitably chosen model.
This is a preview of subscription content, log in via an institution to check access.
References
Akaike, H., “Seasonal Adjustment by a Bayesian Modeling”, Journal of Time Series Analysis, 1980, 1, pp. 1–13.
Beveridge, S., Nelson, C. R., A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the ‘Business Cycle’”, Journal of Monetary Economics, 1981, 7, pp. 151–174.
Campbell, J. Y., Mankiw, N. G., “Permanent and Transitory Components in Macroeconomic Fluctuations”, American Economic Review, Papers and Proceedings, 1987, 77, pp. 111–117.
Cleveland, W. S., Dunn, D. M., Terpenning, I. J., “SABL: A Resistant Seasonal Adjustment Procedure with Graphical Methods for Interpretation and Diagnosis”, in Zellner, A. (Ed.), Seasonal Analysis of Economic Time Series, Bureau of the Census, Economic Research Report, ER-1, Washington, D. C., 1978, pp. 201–241.
Donoho, D. L., Huber, P. J., “The Notion of Breakdown Point”, in Bickel, P. J., et al. (Eds.), Festschrift für Erich L. Lehmann, Wadsworth, Belmont, CA, 1983.
Friedrich, D., “Interpolation, Glättung und Saisonbereinigung von Zeitreihen mit Splinefunktionen”, Statistical Papers, 1984, 25, pp. 13–51.
Hampel, F. R., Stahel, W. A., Ronchetti, E. M., Rousseeuw, P. J., Robust Statistics: The Approach Based on Influence Functions, John Wiley, New York, 1986.
Hebbel, H., Heiler, S., “Trend and Seasonal Decomposition in Discrete Time”, Statistical Papers, 1987, 28, pp. 133–158.
Huber, P. J., “Robust Methods of Estimation of Regression Coefficients”, Mathematische Operationsforschung und Statistik, Series Statistics, 1977, 8, pp. 695–715.
Kitagawa, G., Gersch, W., “A Smoothness Priors-State Space Modeling of Time Series With Trend and Seasonality”, Journal of the American Statistical Association, 1984, 79, pp. 378–389.
Mallows, C. L., “Some Theory of Nonlinear Smoothers”, Annals of Statistics, 1980, 8(4), pp. 695–715.
Müller-Angstenberger, J., “Die Saisonbereinigung wirtschaftlicher Zeitreihen”, Jahrbücher für Statistik und Landeskunde des Landes Baden-Württemberg, 1979, 24, pp. 113–140.
Nagel, G., “Numerical Solution of a Time Series Problem”, Schwerpunkt Mathematisierung der Universität Bielefeld, Materialien, 1982, (15).
Schlicht, E., “A Seasonal Adjustment Principle and a Seasonal Adjustment Method Derived from that Principle”, Journal of the American Statistical Association, 1981, 76, pp. 374–378.
Schlicht, E., “Seasonal Adjustment in a Stochastic Model”, Statistical Papers, 1984, 25, pp. 1–12.
Schlicht, E., Pauly, R., “Descriptive Seasonal Adjustment by Minimizing Perturbations”, Empirica, 1983, 10(1), S. 15–28.
Schlittgen, R., “Robuste Glättung ökonomischer Zeitreihen”, Allgemeines Statistisches Archiv, 1990.
Schlittgen, R., Streitberg, B. H. J., Zeitreihenanalyse, 3. Auflage, Oldenbourg, München-Wien, 1989.
Sen, P. K., “Estimates of the Regression Coefficient Based on Kendall's Tau”, Journal of the American Statistical Association, 1968, 63, pp. 1379–1384.
Theil, H., “A Rank-Invariant Method of Linear and Polynomial Regression Analysis I, II, and III”, Proceedings of Koninklijke Nederlandse Akademie van Wetenschapen, 1950, 53, pp. 386–392, pp. 521–525, pp. 1397–1412.
Tukey, J. W., Explorative Data Analysis, Addison Wesley, Reading, Mass., 1977.
Author information
Authors and Affiliations
Additional information
I am grateful to the referees for several helpful comments and suggestions.
Rights and permissions
About this article
Cite this article
Schlittgen, R. Resistant decomposition of economic time series. Empirica 18, 47–63 (1991). https://doi.org/10.1007/BF00925001
Issue Date:
DOI: https://doi.org/10.1007/BF00925001