## AR(1): the probabilistic reduction perspective

The probabilistic reduction perspective has been developed in Spanos (1986). This perspective begins with the observable process {yt, t Є T} and specifies the statistical model exclusively in terms of this process. In particular, it contemplates the DGM (28.3) from left to right as an orthogonal decomposition of the form:

yt = E(ytc(Y0-i)) + ut, t Є T, (28.9)

where Yt-i := (yt-i, yt-2,…, Уо) and Ut = yt – E(yt o(Yt-i)), with the underlying

statistical model viewed as a reduction from the joint distribution of the underlying process {yt, t Є T}. The form of the autoregressive function depends on:

f(Уо, yv У2,…, yr, v^ for all (yо, Уl, У2,…, Ут) є

in the sense of Kolmogorov (1933)...

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