Hi Duncan, ccf(x,y) does not explain whether c(k)=cov(x(t),x(t+k)) or d(k)=cov(x(t),x(t-k)) is calculated. The following example demonstrates that the c(k) definition is used: ccf(c(-1,1,rep(0,8)),c(1,rep(0,9))) However S-Plus acf uses the d(k) definition in their acf function.
For interpretive purposes this is a **vital distinction** (the cross-covariance/correlation is not symmetric like the autocovariance/autocorrelation). There is not fixed convention is textbooks or research papers. Some define it one way and other another. There is no ccf function in S-Plus. Instead there is only acf for the auto/cross computation in multivariate time series. This is more complicated since numerical output is 3D array. Here is how S-Plus documents it: VALUE: a list with the following components: acf a three-dimensional array containing the autocovariance or autocorrelation function estimates. acf[i,j,k] is the covariance (or correlation) between the j -th series at time t and the k-th series at time t+1-i. lag an array the same shape as acf containing the lags (as fractions of the sampling period) at which acf is calculated. If j > k and i > 1, then lag[i,j,k] is negative. Ian McLeod ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
