KPSS test for stationarity
uses additional options specified by one or more h
= kpsstest(y
,Name,Value
)Name,Value
pair arguments.
If any Name,Value
pair argument is a vector, then all Name,Value
pair arguments specified must be vectors of equal length or length one. kpsstest(y,Name,Value)
treats each element of a vector input as a separate test, and returns a vector of rejection decisions.
If any Name,Value
pair argument is a row vector, then kpsstest(y,Name,Value)
returns a row vector.
In order to draw valid inferences from the KPSS test, you should determine a suitable value for 'lags'
. These two methods determine a suitable number of lags:
Begin with a small number of lags and then evaluate the sensitivity of the results by adding more lags.
Kwiatkowski et al. [2] suggest that a number of lags on the order of , where T is the sample size, is often satisfactory under both the null and the alternative.
For consistency of the Newey-West estimator, the number of lags must approach infinity as the sample size increases.
You should determine the value of 'trend'
by the growth characteristics of the time series. Determine its value with a specific testing strategy in mind.
If a series is growing, then include a trend term to provide a reasonable comparison of a trend stationary null and a unit root process with drift. kpsstest
sets 'trend',true
by default.
If a series does not exhibit long-term growth characteristics, then don’t include a trend term (i.e., set 'trend',false
).
kpsstest
performs a regression to find the ordinary least squares (OLS) fit between the data and the null model.
Test statistics follow nonstandard distributions under the null, even asymptotically. Kwiatkowski et al. [2] use Monte Carlo simulations, for models with and without a trend, to tabulate asymptotic critical values for a standard set of significance levels between 0.01 and 0.1. kpsstest
interpolates critical values and p-values from these tables.
[1] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[2] Kwiatkowski, D., P. C. B. Phillips, P. Schmidt, and Y. Shin. “Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root.” Journal of Econometrics. Vol. 54, 1992, pp. 159–178.
[3] Newey, W. K., and K. D. West. “A Simple, Positive Semidefinite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica. Vol. 55, 1987, pp. 703–708.