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

Question

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?

score 18 · Answer 1 · answered Jul 19 '10 at 23:32

18

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.

answered Jul 19 '10 at 23:32

Rob Hyndman

56,782

Is there a convenient way to determine the order of integration if beyond I(0) or I(1), e.g. I(2) etc.? – Feb 13 '17 at 13:24
5

Difference the data and apply the tests again. – Rob Hyndman Feb 13 '17 at 21:25

score 4 · Answer 2 · answered Jul 20 '10 at 11:14

Also, for some elaborate discussion (including bashing of ADF / PP / KPSS :) you might want to have a look at the book by Maddala and Kim:

http://www.amazon.com/Cointegration-Structural-Change-Themes-Econometrics/dp/0521587824

Quite extensive and not very easy to read sometimes, but a useful reference.

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

2 Answers2