Question: 1) why a time series with trend has usually highly significant autocorrelation function (ACF) in the first few lags and only decays very slowly. I

1) why a time series with trend has usually highly significant autocorrelation function (ACF) in the first few lags and only decays very slowly.

I do understand on a general note that Autocorrection function(ACF) shows how well the present values are related with the past values which is the the reason as to why a time series trend shows a high significance autocorrelation function(ACF) in the first few lags.

It implies that the more recent values show a strong correlation up to a given lag K and then starts to decrease in significance to no correlation. Why is this so?

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