Autocorrelation of detrended values

In many time series, unusually large values tend to be followed by other similar values, even after taking into account the trend in the series. Even after a smooth trend line has been fitted, it is often found that successive detrended values,

ei  =  yi − trendi

are similar in sign and magnitude. This is called autocorrelation.

If autocorrelation exists, it has an important impact on forecasting — if the current value is above the trend line, we should forecast that the next value will also be above it.

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