# #StackBounty: #time-series #stationarity #sas #unit-root #kpss-test Evaluating the importance of a unit-root

### Bounty: 100

I have a monthly time series and I’m trying to determine if such set of data is stationary or not; the dataset is about composed by 160 record.

Specifically, I’m running 2 test found in literature:

1. KPSS: if $$H_0$$ has been rejected then one cannot assume the time series is stationary;
2. Phillips-Perron test: if $$H_0$$ has been rejected then one cannot assume that the time series has a unit-root (then it is stationary);

I preferred to implement the Phillips-Perron test in place of the most common Augmented Dickey-Fuller test since the Phillips-Perron test adjusts for the heteroschedasticity and serial correlation.

Here below, one can find the output of such analysis.

The KPSS test returns not significant p-values both for single-mean, implying that you cannot infer that the time series is not stationary; likewise, the Phillips-Perron test returns significant p-values for the single-mean and trend component, but not for the zero-mean case.

How should I consider or interpret such result?

I wonder if one can evaluate the importance and the strength of such unit-root; for instance, in the question the user @ferdi deals with the variance ratio test to argue the framework to evaluate the importance of a unit root in a time series.

Could you suggest some reference about?

I’m currently running the analysis in SAS, but any programming language would be nice.