# KPSS test - output interpretation in stata

I did KPSS test for some variables in stata to check for stationarity; I want to interpret the the stata outputs, but I don't know how to do that. For instance, in the following case:

    KPSS test for mIlliq1
Maxlag = 13 chosen by Schwert criterion
Autocovariances weighted by Bartlett kernel
Critical values for H0: mIlliq1 is trend stationary
10%: 0.119  5% : 0.146  2.5%: 0.176  1% : 0.216

Lag order    Test statistic
0           .557
1           .309
2           .229
3           .188
4           .162
5           .144
6           .129
7           .118
8           .109
9           .102
10          .0974
11          .0934
12          .0901
13          .0873
Maxlag = 13 chosen by Schwert criterion
Autocovariances weighted by Bartlett kernel


How Can I interpret this result? Does it mean that the TS is stationary or not? If it isn't, how can I can make it a stationary time series? Thank to everyone.

The KPSS test is used for testing a null hypothesis that an observable time series is stationary around a deterministic trend. You can see that the critical values are given by:

 Critical values for H0: mIlliq1 is trend stationary


So as you can see, you cannot reject the H0, that your data is trend-stationary. So the data follow a straight-line time trend with stationary errors.

But since you cannot reject, that only means that there is no evidence that it is not trend stationary; see the discussion here.

The following picture shows what is maybe appropriate for you, a trend-stationary model:

You now

1. Estimate the trend via OLS
2. Use the residuals to fit an ARMA model
3. Check the model (final residuals)

Thats it.

• 0. Plot your series and think about it. – Nick Cox May 1 '13 at 18:40