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Temporal aggregation of cyclical models with business cycle applications

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Abstract

This paper focuses on temporal aggregation of the cyclical component model as introduced by Harvey (1989). More specifically, it provides the properties of the aggregate process for any generic period of aggregation. As a consequence, the exact link between aggregate and disaggregate parameters can be easily derived. The cyclical model is important due to its relevance in the analysis of business cycle. Given this, two empirical applications are presented in order to compare the estimated parameters of the quarterly models for German and US gross domestic products with those of the corresponding models aggregated to annual frequency.

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References

  • Amemiya T, Wu RY (1972) The effect of aggregation on prediction in the autoregressive model. J A Stat Assoc 67: 628–632

    Article  MathSciNet  MATH  Google Scholar 

  • Brewer KRW (1973) Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models. J Econom 1: 133–154

    Article  MATH  Google Scholar 

  • Canova F (2007) Methods for applied macroeconomic research. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Clark PK (1987) The cyclical component of US economic activity. Q J Econ 102: 797–814

    Article  Google Scholar 

  • Doornik JA, Hansen H (1994) An Omnibus test for univariate and multivariate normality. Economics working papers W4 & 91, Nuffield College

  • Harvey AC (1989) Forecasting structural time series and the Kalman filter. Cambridge University Press, Cambridge

    Google Scholar 

  • Harvey AC, Jaeger A (1993) Detrending, stylised facts and the business cycle. J Appl Econom 8: 231–247

    Article  Google Scholar 

  • Hassler U (2011) Estimation of fractional integration under temporal aggregation. J Econom 162: 240–247

    Article  MathSciNet  Google Scholar 

  • Hodrick RJ, Prescott EC (1997) Postwar US business cycles: an empirical investigation. J Money Credit Bank 29: 1–16

    Article  Google Scholar 

  • Hotta LK, Vasconcellos KL (1999) Aggregation and disaggregation of structural time series models. J Time Ser Anal 20: 155–171

    Article  MathSciNet  Google Scholar 

  • Koopman SJ, Harvey AC, Doornik JA, Shephard N (2007) STAMP 8.2 structural time seires analyser, modeller and predictor. Timberlake Consultants Ltd, London

    Google Scholar 

  • Luati A, Proietti T (2010) Hyper-spherical and elliptical stochastic cycles. J Time Ser Anal 31: 169–181

    Article  MathSciNet  MATH  Google Scholar 

  • del Maravall A, Rio A (2007) Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter. Comput Stat Data Anal 52: 975–998

    Article  MATH  Google Scholar 

  • Proietti T (2000) Comparing seasonal components for structural time series models. Int J Forecast 16: 247–260

    Article  Google Scholar 

  • Sbrana G (2011) Structural time series models and aggregation: some analytical results. J Time Ser Anal 32: 315–316

    Article  MathSciNet  Google Scholar 

  • Silvestrini A, Veredas D (2008) Temporal aggregation of univariate and multivariate time series models: a survey. J Econ Surv 22: 458–497

    Article  Google Scholar 

  • Stram DO, Wei WWS (1986) Temporal aggregation in the ARIMA process. J Time Ser Anal 7: 279–292

    Article  MathSciNet  MATH  Google Scholar 

  • Wei WWS (1978) Some consequences of temporal aggregation in seasonal time series models. In: Zellner A (ed) Seasonal analysis of economic time series. US Department of Commerce, Bureau of the Census, pp 433–444

    Google Scholar 

  • Weiss A (1984) Systematic sampling and temporal aggregation in time series models. J Econom 26: 271–281

    Article  Google Scholar 

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Authors and Affiliations

  1. Rouen Business School, 1 Rue du Maréchal Juin, BP215, 76825, Mont Saint Aignan Cedex, France

    Giacomo Sbrana

  2. Bank of Italy, Economics, Research and International Relations, Via Nazionale 91, 00184, Rome, Italy

    Andrea Silvestrini

Authors
  1. Giacomo Sbrana
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  2. Andrea Silvestrini
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Correspondence to Andrea Silvestrini.

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Sbrana, G., Silvestrini, A. Temporal aggregation of cyclical models with business cycle applications. Stat Methods Appl 21, 93–107 (2012). https://doi.org/10.1007/s10260-011-0181-0

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  • DOI: https://doi.org/10.1007/s10260-011-0181-0

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