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Transformations and seasonal adjustment

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  • Tommaso Proietti
  • Marco Riani

Abstract

We address the problem of seasonal adjustment of a nonlinear transformation of the original time series, measured on a ratio scale, which aims at enforcing two essential features: additivity and orthogonality of the components. The posterior mean and variance of the seasonally adjusted series admit an analytic finite representation only for particular values of the transformation parameter, e.g. for a fractional Box-Cox transformation parameter. Even if available, the analytical derivation can be tedious and difficult. As an alternative we propose to compute the two conditional moments of the seasonally adjusted series by means of numerical and Monte Carlo integration. The former is both fast and reliable in univariate applications. The latter uses the algorithm known as the 'simulation smoother' and it is most useful in multivariate applications. We present two case studies dealing with robust seasonal adjustment under the square root and the fourth root transformation. Our overall conclusion is that robust seasonal adjustment under transformations is feasible from the computational standpoint and that the possibility of transforming the scale ought to be considered as a further option for improving the quality of seasonal adjustment. Copyright 2009 The Authors. Journal compilation 2009 Blackwell Publishing Ltd

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 30 (2009)
Issue (Month): 1 (01)
Pages: 47-69

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Handle: RePEc:bla:jtsera:v:30:y:2009:i:1:p:47-69

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782

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Cited by:
  1. Tommaso Proietti & Helmut Luetkepohl, 2011. "Does the Box-Cox Transformation Help in Forecasting Macroeconomic Time Series?," Economics Working Papers ECO2011/29, European University Institute.
  2. Siem Jan Koopman & Kai Ming Lee, 0000. "Seasonality with Trend and Cycle Interactions in Unobserved Components Models," Tinbergen Institute Discussion Papers 08-028/4, Tinbergen Institute.

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