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Centered and noncentered moving averages: Construction and Comparison. (Moyennes mobiles centrées et non-centrées: construction et comparaison.) (French) Zbl 0972.62538
Summary: In the first part of the paper we present an overview of the various moving averages which, thanks to their efficiency and simplicity, still remain an important tool for the statistician who wants to perform smoothing or seasonal adjustment. In the second part, the construction of centered or non-centered moving averages is then seen as a problem of optimization under constraints. This point of view enables us to answer the question of the loss of information at the extremities of the time series. Incidentally, the equivalence of the approach proposed by Kendall and Bongard is proved. The Musgrave asymmetric moving averages, used in the X11 software, are replaced in this context and then generalized. A new convex criterion is defined using the Bongard and Henderson criteria and then studied via a simple example.
MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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References:
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