8.1 Unit Roots

Recall from section 6.1, TS consist of four elements: T,S,C,I.

T,S and C are what is called determistic components. Where the rest, I, is irregular, although this might contain some properties as well. These properties are called stochastic or random properties

Definition on stochastic: having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely.

In this chapter, we explore how a time-series that visually does not reflect nonstationary data, can in fact be non stationary.

One may observe, that even though the irregular component is often random (being stationary), it may have show nonstationarity.

In general, one can do unit root tests, to test if the data is stationary or non stationary. In general, it can be said:

Unit Root = Non Stationarity

Hence; I have found unit roots in the data = i have found non stationarity
in the data

The following will explore how Augmented Dickey-Fuller test (ADF) can make an assessment of unit roots.

8.1.1 Augmented Dickey-Fuller (ADF) test

This is basically a test for nonstationarity.

Null hypothesis = x has a unit root (i.e. is non stationary) Alternate hypothesis = x has not unit root (i.e. is stationary)

Be careful, this test may contradict with the Durbin-Watson test, if the variables actually do appear to be cointegrated

Side note: but the variables may not be stationary, but if they are not spuriously related, hence cointegrated, then it is in fact OK for the variables to have stationarity

See the equation for the ADF in the slides from L11.

See exercise 8.4.1.1 with the Dairy Data.