To quote Barnett (2006), the Slutsky effect, as understood by most economists, is the following:

If the variables that were taken to represent business cycles were moving averages of past determining quantities that were not serially correlated – either real-world moving averages or artificially generated moving averages – then the variables of interest would become serially correlated, and this process would produce a periodicity approaching that of sine waves.

I wrote a short note using SageTeX demonstrating the effect, closely following Royoma’s book (look at the price!!!).

My note: slutsky_effect.tex, or slutsky_effect.pdf

Two useful papers (click for PDF):

Barnett, Vincent (2006). “Chancing an Interpretation: Slutsky’s Random Cycles Revisited”, European Journal of the History of Economic Thought, 13 (3): 411-32.

Slutsky, 1937. The summation of random causes as the source of cyclic processes. Econometrica 1937;5:105-46.