Transformations and Seasonal Adjustment

23 Pages Posted: 2 Jan 2009

See all articles by Tommaso Proietti

Tommaso Proietti

University of Rome II - Department of Economics and Finance

Marco Riani

University of Parma

Date Written: 0000


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 BoxCox 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.

Suggested Citation

Proietti, Tommaso and Riani, Marco, Transformations and Seasonal Adjustment (0000). Journal of Time Series Analysis, Vol. 30, Issue 1, pp. 47-69, January 2009. Available at SSRN: or

Tommaso Proietti

University of Rome II - Department of Economics and Finance ( email )

Via Columbia, 2
Rome, 00133

Marco Riani

University of Parma ( email )

Via Amendola 10
Parma, 43100
United States

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