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I'm working on multivariate time series (still), and would like some clarification. I was reading this site: Duke Forecasting and I came across this statement:

"We see that the most significant cross-correlation is at lag 0, but unfortunately we cannot use that for forecasting one month ahead. Instead, we must try to exploit the smaller cross-correlations at lags 1 and/or 2. "

Not wanting to read too much into that, am I correct in understanding that if that using the pre-whiten function identifies a significant cross-correlation between x and y, and that the most significant lag is at time = 0, then that variable basically adds nothing to our ability to forecast y (and could be dropped). If so, why?

counter argument - many transfer functions have significant AR and MA terms with no delay (lag = 0).

Welcome any discussion! Thanks!

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