R中的互相关方式

Question

For cross correlation of a bivariate time series, I use either ccf or acf to plot it, but the two plots are not the same. The first plot by ccf agrees with the lefttop plot of acf , while the second plot by ccf doesn't agree with the rightbottom plot of acf .

I wonder if I miss something? Thanks!

par(mfrow = c(2,1))
ccf(x[,1],x[,2])     
ccf(x[,2],x[,1])     

acf(x)  

Answer 1

ACF measures correlations of a single time series against its own lags. CCF measures correlations between two time series at different lags. What appears to be the same (first plot by ccf and the lefttop plot of acf) are actually different. If you pulled out the values, I am sure you would see this. If the two time-series have a high correlation, it is very likely that the ACF and CCF would appear to be the same.

The first plot of the CCF actually matches the bottomleft ACF plus topright ACF combined. The top left and bottom right ACF plots express only univariate time-series lag correlations.

If you enter a multivariate timeseries into the ACF function, it will return the auto-correlation plots (top-left and bottom-right) along with the two halves of the cross-correlation function.