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Estimating Trends with Percentage of Smoothness Chosen by the User

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  • Victor M. Guerrero

Abstract

This work presents a method for estimating trends of economic time series that allows the user to fix at the outset the desired percentage of smoothness for the trend. The calculations are based on the Hodrick‐Prescott (HP) filter usually employed in business cycle analysis. The situation considered here is not related to that kind of analysis, but with describing the dynamic behaviour of the series by way of a smooth curve. To apply the filter, the user has to specify a smoothing constant that determines the dynamic behaviour of the trend. A new method that formalizes the concept of trend smoothness is proposed here to choose that constant. Smoothness of the trend is measured in percentage terms with the aid of an index related to the underlying statistical model of the HP filter. Empirical illustrations are provided using data on Mexico's GDP. Ce travail présente un méthode pour estimer les tendances des séries de temps économiques qui permet à l'usager fixer dès début le pourcentage désiré de douceur pour la tendance. Les calculs ont fondement en le filtre de Hodrick et Prescott que s'emploie généralement dans l'analyse de cycles économiques. La situation ici considéré n'a pas relation avec ce type d'analyse, mais comment la description du comportement dynamique des séries avec une courbe douce. Pour appliquer le filtre, l'usager a besoin de spécifier une constante de douceur que détermine le comportement dynamique de la tendance. Un nouveau méthode que formalise le concept de douceur de la tendance est ici proposé pour choisir la constante. La douceur de la tendance est mesuré en termes de pourcentage avec l'aide d'un index rapporté avec le modèle statistique après le filtre. Quelques illustrations empiriques sont munies avec données de l'économie mexicaine.

Suggested Citation

  • Victor M. Guerrero, 2008. "Estimating Trends with Percentage of Smoothness Chosen by the User," International Statistical Review, International Statistical Institute, vol. 76(2), pages 187-202, August.
    • Handle: RePEc:bla:istatr:v:76:y:2008:i:2:p:187-202
    DOI: 10.1111/j.1751-5823.2008.00047.x
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    References listed on IDEAS

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    Cited by:

    1. A. ISLAS & Víctor M. GUERRERO & Eliud SILVA, 2019. "Forecasting Remittances to Mexico with a Multi-State Markov-Switching Model Applied to the Trend with Controlled Smoothness," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 38-56, March.
    2. Víctor M. Guerrero & Adriana Galicia‐Vázquez, 2010. "Trend estimation of financial time series," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 205-223, May.
    3. Víctor M. Guerrero & Daniela Cortés Toto & Hortensia J. Reyes Cervantes, 2018. "Effect of autocorrelation when estimating the trend of a time series via penalized least squares with controlled smoothness," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 109-130, March.
    4. Eliud Silva & Víctor M. Guerrero, 2017. "Penalized least squares smoothing of two-dimensional mortality tables with imposed smoothness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1662-1679, July.

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