KPSS—Kwiatowksi et al Unit Root Test

[TomDoan]

@KPSS performs the KPSS test from Kwiatowski, Phillips, Schmidt & Shin(1992), "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?", J. of Econometrics, vol 54, pp 159-178. Unlike most unit root tests, this has the null of stationarity (around a constant or trend) and rejects if the series is more persistent than would be compatible with stationarity. The KPSS test is on the Unit Root Test wizard on the Time Series menu.

Detailed description

Example

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*
* Greene, Econometric Analysis, 7th Edition
* Example 23.3 and 23.4 from pp 1026-1028
*
open data tablef5-2.txt
calendar(q) 1950
data(format=prn,org=columns) 1950:01 2000:04 year qtr realgdp realcons $
 realinvs realgovt realdpi cpi_u m1 tbilrate unemp pop infl realint
*
set loggdp  = log(realgdp)
*
* ADFAutoSelect does a sequence of DF tests and displays a table of
* criteria which can be used to select the lag length. The final column
* has the test statistic. This differs from  the one in the stand-alone
* DFUNIT because ADFAutoSelect uses only the data points allowed when 14
* lags are included, while DFUNIT (by default), uses the maximum range
* allowed with the number of lags used on it.
*
@adfautoselect(maxlags=14,det=trend,print) loggdp
@dfunit(lags=1,det=trend) loggdp
*
@ppunit(lags=4,det=trend) loggdp
*
* KPSS test (example 22.4)
*
@kpss(lags=10,det=constant) loggdp
@kpss(lags=10,det=trend) loggdp

TableF5-2.txt

Data file for example

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Sample Output

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KPSS Test for Stationarity about Trend, Series LOGGDP
From 1950:01 to 2000:04
Observations 204

Sig Level Crit Value
1%(**)    0.216000
2.5%      0.176000
5%(*)     0.146000
10%       0.119000

  Lags    TestStat
       10 0.311579**

Because the null is that the series is trend-stationary, this rejects that in favor of a unit root.

[sarthak24]

Dear Tom

For the KPSS test, how can one know what is the appropriate no. of lags? Does there exist a procedure (like ADFAUTOSELECT is for ADF test) to ascertain this? Does there exist a criteria (like AIC or SIC) for deciding the appropriate no. of lags?

Many thanks.

[TomDoan]

No. The KPSS lags aren't optimizing anything, so there's no equivalant of AIC or SBC to guide the selection. Typically, you see whether there is any sensitivity to the choice. Typically, there isn't once you get "enough". (Short lags often give very different test values than somewhat longer ones, but at some point the test statistics tend to stabilize).