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This paper owes much to many discussions with R. Pauly. He pointed out that the descriptive methods under discussion can be turned into statistical models by introducing a suitable parametrization. He proposed the parametrization by initial values as described in Pauly [1982]; see also Pauly/Schlicht [1984]. This induced the idea of the alternative parametrization developed in this paper. In contrast to other attempts in this direction— notably by Akaike [1980] and Pauly [1982]—the estimation procedure does not involve initial values. Hence the asymmetry in the estimation procedure associated with the introduction of initial values is avoided and a “weakly symmetric” decomposition is obtained [see Schlicht/Pauly, 1984, section 5.]. On the Schlicht/Pauly procedure and numerical results, see also Astier/Duhamel [1982].
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Schlicht, E. Seasonal adjustment in a stochastic model. Statistische Hefte 25, 1–12 (1983). https://doi.org/10.1007/BF02932388
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DOI: https://doi.org/10.1007/BF02932388