CORRELATION OF FIRST DIFFERENCES 917 differences between terms correspondingly positioned in each segment Aum)= Xi-Xi-m, these first differences will have a variance var(4 But suppose that we now average the m terms in each segment of the chain and take first differences between the averages Am=1(x+x+1..+x4+m)-1(xm+x E一+1 +Xt-1) sing the relationship in(1), as illustrated in the tabulation above, this may be written, with reversal of the order of terms in the second parenthesis above (m)=mX+(x4+4+)…+(x4+1+4+2…+b+m-1 [(X4-0)+(Xt-0-b4-1)..+(X-b-0 and then simplified to 彡们 A +b4+m-1+mbx+(m-1) +-m+1] Then, bearing in mind that the 8s are all mutually uncorrelated and have been assigned a variance of unity, we may derive var(di(m)) (m-1)2+(m-2)2.,+12+m2+(m-1 thich reduces to var Comparison of expression (4)with expression(2)shows that, with m only moderately large, the variance of first differences between averages over successive segments of a random chain approximates 2/3 of the variance of first differences between correspondingly positioned terms in the chain The covariance of successive first differences between averages may be written as, cov(4((m), 4(-m)(m)), which suggests that the covariance may be derived from the product of expression (3)multiplied by (5)4(-m)m[(m-1)b1-m+1+(m-2)5-m+2+ b-1+mb-m+(m-1)04-m-1+