Econometrica, Vol 28, 4(October 1960) NOTE ON THE CORRELATION OF FIRST DIFFERENCES OF AVERAGES IN A RANDOM CHAIN BY HOLBROOK WORKING IN THE STUDY of serial correlations in prices series it is important to bear in mind that the use of averages can introduce correlations not present in in the original series. II consider here the effect of averaging successive groups of items in a random chain, which is the simplest sort of stochastic series to which stock prices and certain commodity prices have a close resemblance The equation for a random chain may be written (1)x4=X4-1+b(i=1,2,…;E(6)=0;cor(5,04+)=0 when 1≠0), where Xi-1, Xi are successive terms in the chain. In what follows I assume further, for convenience and without loss of generality, that var(8)=I Consider now a random chain that is treated as being composed of successive segments of m items each, corresponding to weeks, months or any other time intervals, in a price series, For purposes of illustration we may take m =3 and write the terms of three successive segments of a random chain by derivation from the 8s as follows 4 6;=+20-11-0.6+0.3+1.3-1.0+0.1+07-0.3 Xt=24443.327 3.0 It is obvious that if, from this segmented random chain, we take first 1 One example of the need is cited in the paper by Alfred Cowles elsewhere in this ssue of Econometrica. Another example is afforded by M. G. Kendall's conclusion that wheat prices and cotton prices have behaved differently, as evidenced by a first order serial correlation of first differences, n1 = +0.313, for cotton prices as against a corresponding coefficient, n1 =-0.071, for wheat prices( "The Analysis of Economic me-Series, "Journal of the Royal Statistical Society, CXVI(1953), pp. 15, 23). Because the cotton-price series that Kendall used consisted of monthly averages of, for the most part, daily prices, a serial correlation of about=+0.25 in the cotton price series was to have been expected simply as a result of the averaging process, as I show below.The wheat price series that Kendall used, on the other hand, was one that I had compiled without averaging, in order to avoid introducing the averaging effect Vhen this difference in constitution of the two series is taken into account there remains no clear evidence of difference in behaviour between wheat prices and cotton prices The example is from Holbrook Working, " A Random-Difference Series for Use in the Analysis of Time Series, " Journal of the American Statistical A ssociation, March, 934, taking the last figure in the second column of the table as Xo, but with al figures divided by 10 in order to have var(dx)=I 916