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Décomposition tendance-cycle : estimations par des méthodes statistiques univariées

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  • Nicolas Sobczak
  • Guillaume Rabault
  • Catherine Doz

Abstract

[fre] L'analyse des séries macro-économiques repose généralement sur une décomposition en tendance et cycle. Cet article est consacré à l'examen de méthodes purement statistiques d'extraction d'une tendance et d'un cycle à partir d'une série brute ; il se limite aux techniques univariées les plus fréquemment utilisées. Après une présentation des techniques traditionnelles, on introduit des méthodes de décomposition dans lesquelles la tendance est explicitement modélisée comme un processus stochastique. On présente en particulier la décomposition de Beveridge-Nelson et les modèles à composantes inobservables, et on applique ces méthodes sur données françaises. Parmi les modèles présentés, seuls ceux qui spécifient une tendance intégrée d'ordre 2 conduisent à une composante cyclique présentant une certaine amplitude. Nous analysons alors ce résultat d'un point de vue théorique. [spa] Desgloses tendencia - ciclo : estimación mediante métodos estadísticos univariados por Catherine Doz, Guillaume Rabault y Nicolas Sobczak . El análisis de las series macroeconômicas descansa por lo general en un desglose en tendencia y ciclo. Este articulo esta dedicado al examen de métodos puramente estadisticos de extracciôn de una tendencia y de un ciclo a partir de una série bruta ; se limita a las técnicas univariadas que con mas frecuencia se utilizan. Después de una presentacion de las técnicas tradicionales, se introduce métodos de desglose en los cuales la tendencia esta explicitamente modelizada como un proceso estocâstico. Se présenta en particular el desglose de Beveridge-Nelson, y los modelos de componentes inobservables y se aplica estes métodos a datos franceses. Entre los modelos presentados, solo aquellos que especifican una tendencia integrada de orden 2 conducen a un componente ciclico que présenta una cierta amplitud. Analizamos entonces dicho resultado desde un punto de vista teôrico. [ger] Zerlegungen in Trend und Zyklus: Schätzung mit univariaten statistischen Methoden von Catherine Doz, Guillaume Rabault, Nicolas Sobczak . Die Analyse der gesamtwirtschaftlichen Reihen beruht im allgemeinen auf einer Zerlegung in Trend und Zyklus. In diesem Artikel werden rein statistische Methoden zur Herausrechnung eines Trends und eines Zyklus anhand einer Bruttoreihe untersucht. Hierbei beschranken wir uns auf die am haufigsten verwandten univariaten Verfahren. Nach einer Darstellung der herkommlichen Verfahren werden Zerlegungsmethoden mit einbezogen, bei denen der Trend explizit als stochastischer ProzeB modelliert wird. Erlautert werden insbesondere die Zerlegungsformel von Beveridge-Nelson sowie die Modelle mit nichtbeobachtbaren Komponenten, wobei diese Methoden auf franzôsische Daten angewandt werden. Unter den dargestellten Modellen fuhren lediglich diejenigen, die einen integrierten Trend zweiter Ordnung spezifizieren, zu einer zyklischen Komponente, die eine gewisse Amplitude aufweist. Dieses Ergebnis analysieren wir anschlieBend in theoretischer Hinsicht. [eng] Trend-Cycle Breakdown: Estimations Using Univariate Statistical Methods by Catherine Doz, Guillaume Rabault and Nicolas Sobczak . The analysis of macroeconomic series is generally based on a breakdown into trend and cycle. This paper examines the purely statistical methods of trend and cycle extraction from a complete series. It is limited to the most frequently used univariate techniques. Once the traditional techniques have been presented, the breakdown methods are introduced whereby the trend is explicitly modeled as a stochastic process. Special attention is paid to the Beveridge-Nelson breakdown and the models with unobservable components. These methods are then applied to French data. Of the models presented, only those specifying a trend integrated of order two result in a cyclical component of some magnitude. This result is analyzed from a theoretical point of view.

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Bibliographic Info

Article provided by Programme National Persée in its journal Économie & prévision.

Volume (Year): 120 (1995)
Issue (Month): 4 ()
Pages: 73-93

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Handle: RePEc:prs:ecoprv:ecop_0249-4744_1995_num_120_4_5746

Note: DOI:doi:10.3406/ecop.1995.5746
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Web page: http://www.persee.fr/web/revues/home/prescript/revue/ecop

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  1. Clark, Peter K, 1987. "The Cyclical Component of U.S. Economic Activity," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 797-814, November.
  2. Nelson, Charles R & Kang, Heejoon, 1979. "Spurious Periodicity in Inappropriately Detrended Time Series," The Warwick Economics Research Paper Series (TWERPS) 161, University of Warwick, Department of Economics.
  3. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  4. Alexandre Mathis & Jacky Fayolle, 1993. "Tendances et cycles stylisés dans les pays du G7 - Une approche stochastique," Revue de l'OFCE, Programme National Persée, vol. 47(1), pages 201-233.
  5. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
  6. Danthine, Jean-Pierre & Girardin, Michel, 1989. "Business cycles in Switzerland : A comparative study," European Economic Review, Elsevier, vol. 33(1), pages 31-50, January.
  7. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
  8. Quah, Danny, 1992. "The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds," Econometrica, Econometric Society, vol. 60(1), pages 107-18, January.
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