D.S.G. POLLOCK : THE METHODS OF TIME-SERIES ANALYSISThe identity∑tcos(ωjt)(yt-¯y) =∑tcos(ωjt)ytfollows from the fact that,by construction,∑tcos(ωjt) = 0 for allj. Hence the above expression has thesame value as the expression in (2). Expanding the expression in (vii) gives(viii)I(ωj) =2T‰XtXscos(ωjt) cos(ωjs)(yt-¯y)(ys-¯y)+2T‰XtXssin(ωjt) sin(ωjs)(yt-¯y)(ys-¯y),and, by using the identity cos(A) cos(B) + sin(A) sin(B) = cos(A-B), we canrewrite this as(ix)I(ωj) =2T‰XtXscos(ωj[t-s])(yt-¯y)(ys-¯y).Next, on definingτ=t-sand writingcτ=∑t(yt-¯y)(yt-τ-¯y)/T, we canreduce the latter expression to(x)I(ωj) = 2T-1Xτ=1-Tcos(ωjτ)cτ,which appears in the text as equation (15).References[1] Alberts, W. W., L. E. Wright and B. Feinstein (1965), “PhysiologicalMechanisms of Tremor and Rigidity in Parkinsonism.”Confinia Neuro-logica, 26, 318–327.[2] Beveridge, Sir W. H. (1921), “Weather and Harvest Cycles.”EconomicJournal, 31, 429–452.[3] Beveridge, Sir W. H. (1922), “Wheat Prices and Rainfall in Western Eu-rope.” Journal of the Royal Statistical Society, 85, 412–478.[4] Box, G. E. P. and D. R. Cox (1964), “An Analysis of Transformations.”Journal of the Royal Statistical Society, Series B, 26, 211–243.[2] Box, G. E. P. and G. M. Jenkins (1970), Time Series Analysis, Forecastingand Control. Holden–Day: San Francisco.[6] Buys–Ballot, C. D. H. (1847), “Les Changements Periodiques de Temper-ature.” Utrecht.[7] Cooley, J. W. and J. W. Tukey (1965), “An Algorithm for the MachineCalculation of Complex Fourier Series.” Mathematics of Computation, 19,297–301.17