Statistical determination of the nearest type trend for realizations of non-stationary time series
The problem of statistical assignment of realizations X = {x<sub>t</sub>}T<sub>t</sub>=1 of non-stationary time series to the nearest trend model is studied. Here, these trend models {Ωl}l<sub>є</sub>s (S = {1,...,L}, L ≥ 2) are determined by their basic trends {fl(•)}l Є s :∑T<sub>t</sub>=0, l є S, and constitute shift families: f<sup>a</sup>l (t) = fl (t) + a, t = 1, T, where a є R is the shift parameter (l є S). For the decision making, the decision rule by the least-squares method is proposed and its efficiency is analytically investigated (as an efficiency measure its risk is evaluated). For illustration of the obtained results, the case of two alternative trend models is given.