What methods can be used to determine the Order of Integration of a time series?

Econometricians often talk about a time series being integrated with order k, I(k). k being the minimum number of differences required to obtain a stationary time series.

What methods or statistical tests can be used to determine, given a level of confidence, the order of integration of a time series?


There are a number of statistical tests (known as “unit root tests”) for dealing with this problem. The most popular is probably the “Augmented Dickey-Fuller” (ADF) test, although the Phillips-Perron (PP) test and the KPSS test are also widely used.

Both the ADF and PP tests are based on a null hypothesis of a unit root (i.e., an I(1) series). The KPSS test is based on a null hypothesis of stationarity (i.e., an I(0) series). Consequently, the KPSS test can give quite different results from the ADF or PP tests.

Source : Link , Question Author : brotchie , Answer Author : Rob Hyndman

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