{smcl}
{* 19oct2004}{...}
{hline}
help for {hi:kpss}{right:(SJ6-3: sts15_2; STB-58: sts15.1; STB-57: sts15)}
{hline}

{title:Kwiatkowski-Phillips-Schmidt-Shin test for stationarity}

{p 8 17 2}
{cmd:kpss}
{varname}
{ifin}
[{cmd:,} {opt maxlag(#)} {opt not:rend} {opt qs} {opt auto}]

{phang}
{cmd:kpss} is for use with time-series data.  {varname} may contain
time-series operators.  You must {helpb tsset} your data before using
{cmd:kpss}. 

{phang}
{cmd:kpss} supports the {helpb by} prefix, which may be used to operate on
each time series in a panel. Alternatively, the {cmd:if} qualifier may be used
to specify one time series in a panel.


{title:Description}

{pstd}
{cmd:kpss} performs the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS, 1992)
test for stationarity of a time series. This test differs from those "unit
root" tests in common use (such as {helpb dfuller}, {helpb pperron}, and
{helpb dfgls}) by having a null hypothesis of stationarity. The test may be
conducted under the null of either trend stationarity (the default) or level
stationarity.  Inference from this test is complementary to that derived from
those based on the Dickey-Fuller distribution (such as {cmd:dfuller},
{cmd:pperron}, and {cmd:dfgls}). The KPSS test is often used in conjunction
with those tests to investigate the possibility that a series is fractionally
integrated (that is, neither I(1) nor I(0)); see Lee and Schmidt (1996). As
such, it is complementary to {cmd:gphudak}, {cmd:modlpr}, and
{cmd:roblpr}.

{pstd}
The test's denominator--an estimate of the long-run variance of the 
time series, computed from the empirical autocorrelation function--may 
be calculated using either the Bartlett kernel, as employed
by KPSS, or the quadratic spectral kernel. Andrews (1991) and Newey
and West (1994) indicate that the latter kernel yields more accurate 
estimates of sigma-squared than other kernels in finite samples.
(Hobijn et al., 1998, 6)

{pstd}
The maximum lag order for the test is by default calculated from the sample
size using a rule provided by Schwert (1989) using c=12 and d=4 in his
terminology. The maximum lag order may also be provided with the {cmd:maxlag()}
option and may be zero. If the maximum lag order is at least one, the test 
is performed for each lag, with the sample size held constant over lags 
at the maximum available sample.

{pstd}
Alternatively, the maximum lag order (bandwidth) may be derived from an
automatic bandwidth selection routine, rendering it unnecessary to evaluate 
a range of test statistics for various lags. Hobijn et al. (1998) found
that the combination of the automatic bandwidth selection option and the 
quadratic spectral kernel yielded the best small sample test performance
in Monte Carlo simulations.{p_end}

{pstd}
Approximate critical values for the KPSS test are taken from
Kwiatkowski, Phillips, Schmidt, and Shin (1992)

{pstd}
The KPSS test statistic for each lag is placed in the return array.


{title:Options}

{phang}
{opt maxlag(#)} specifies the maximum lag order to be used in
calculating the test. If omitted, the maximum lag order is calculated as
described above.

{phang}
{opt notrend} indicates that level stationarity, rather than trend
stationarity, is the null hypothesis.

{phang}
{opt qs} specifies that the autocovariance function is to be weighted by the 
quadratic spectral kernel, rather than the Bartlett kernel.

{phang}
{opt auto} specifies that the automatic bandwidth selection procedure proposed
by Newey and West (1994) as described by Hobijn et al. (1998, 7) is used to
determine {cmd:maxlag()}. Here one value of the test statistic is produced at
the optimal bandwidth.


{title:Examples}

{p 4 8 2}{stata "use http://fmwww.bc.edu/ec-p/data/macro/nelsonplosser.dta":. use http://fmwww.bc.edu/ec-p/data/macro/nelsonplosser.dta}{p_end}
	
{p 4 8 2}{stata "kpss lrgnp":. kpss lrgnp}{p_end}

{p 4 8 2}{stata "kpss D.lrgnp, maxlag(8) notrend":. kpss D.lrgnp, maxlag(8) notrend}{p_end}
	
{p 4 8 2}{stata "kpss lrgnp if tin(1910,1970)":. kpss lrgnp if tin(1910,1970)}{p_end}
	
{p 4 8 2}{stata "kpss lrgnp, qs auto":. kpss lrgnp, qs auto}{p_end}


{title:Author}

{p 4 4 2}Christopher F. Baum, Boston College, USA{break} 
       baum@bc.edu
       

{title:References}
      
{phang}Andrews, D. W. K.  1991. Heteroskedasticity and autocorrelation
consistent covariance matrix estimation. {it:Econometrica} 59: 817-858.

{phang}Hobijn, B., P. H. Franses, and M. Ooms. 1998. Generalizations
of the KPSS-test for stationarity. Econometric Institute Report 9802/A, 
Econometric Institute, Erasmus University Rotterdam.
{browse "http://www.feweb.vu.nl/econometricLinks/ooms/papers/ei9802.pdf"}.

{phang}Kwiatkowski, D., P. C. B Phillips, P. Schmidt, and Y. 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?
{it:Journal of Econometrics} 54: 159-178.

{phang}Lee, D., and P. Schmidt. 1996. On the power of the KPSS test of
stationarity against fractionally-integrated alternatives.
{it:Journal of Econometrics} 73: 285-302.

{phang}Newey, W. K., and K. D. West. 1994. Automatic lag selection in
covariance matrix estimation. {it:Review of Economic Studies} 61:
631-653.

{phang}Schwert, G. W. 1989. Tests for unit roots: A Monte Carlo investigation.
{it:Journal of Business and Economic Statistics} 7: 147-160.


{title:Acknowledgments}

{pstd}
A version of this code written in the RATS programming language by
John Barkoulas served as a guide for the development of the Stata code.
Thanks to Richard Sperling for suggesting its validation against the 
Nelson-Plosser data (Kwiatkowski, Phillips, Schmidt, and Shin 1992, table 5).


{title:Also see}

{psee}Online: {helpb dfuller}, {helpb pperron}, {help time}, {helpb tsset}, 
{helpb dfgls}, {helpb gphudak} (if installed), {helpb modlpr} (if 
installed), {helpb roblpr} (if installed){p_end}