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Practical Time Series Analysis by Dr. PKS Prakash, Dr. Avishek Pal

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Second-order differencing

In some cases, first-order differencing does not stationarize the time series and therefore the data is differenced another time to generate a stationary time series. Therefore, the second-order differenced time series is generated as follows:

x"t = x't - x't-1 = (xt - xt-1) - (xt-1 - xt-2) = xt - 2xt-1+xt-2

The time series resulting from second-order differencing have N - 2 observations. It is almost never required to perform differencing of order higher than second order.

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