KPSS test - output interpretation in stata

Question

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.

Answer 1

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.