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Akaike is cool


Today I came across a paper in my files, “On a limiting process which asymptotically produces f^{-2} spectral density” from 1962 by Hirotugu Akaike (most famous for his information criterion). The paper has a great opening paragraph:

In the recent papers in which the results of the spectral analyses of roughnesses of runways or roadways are reported, the power spectral densities of approximately the form f^{-2} (f: frequency) are often treated. This fact directed the present author to the investigation of the limiting process which will provide the f^{-2} form under fairly general assumptions. In this paper a very simple model is given which explains a way how the f^{-2} form is obtained asymptotically. Our fundamental model is that the stochastic process, which might be considered to represent the roughness of the runway, is obtained by alternative repetitions of roughening and smoothing. We can easily get the limiting form of the spectrum for this model. Further, by taking into account the physical meaning of roughening and smoothing we can formulate the conditions under which this general result assures that the f^{-2} form will eventually take place.

It’s a cool paper, less than 5 pages long. Something about this reminds me of Mandelbrot’s early papers on taxonomy and Pareto distributions, written about the same time.