lmctest
LeybourneMcCabe stationarity test
Syntax
h
= lmctest(y
)
h
= lmctest(y
,'ParameterName
',ParameterValue
)
[h
,pValue
]
= lmctest(...)
[h
,pValue
,stat
]
= lmctest(...)
[h
,pValue
,stat
,cValue
]
= lmctest(...)
[h
,pValue
,stat
,cValue
,reg1
]
= lmctest(...)
[h
,pValue
,stat
,cValue
,reg1
,reg2
]
= lmctest(...)
Description
assesses
the null hypothesis that
a univariate time series h
= lmctest(y
)y
is a trend stationary
AR(p) process, against the alternative that it
is a nonstationary ARIMA(p,1,1) process.
accepts
one or more commaseparated parameter name/value pairs. Specify h
= lmctest(y
,'ParameterName
',ParameterValue
)ParameterName
inside
single quotes. Perform multiple tests by passing a vector value for
any parameter. Multiple tests yield vector results.
[
returns pvalues of the
test statistics.h
,pValue
]
= lmctest(...)
[
returns the test statistics.h
,pValue
,stat
]
= lmctest(...)
[
returns critical values for the tests.h
,pValue
,stat
,cValue
]
= lmctest(...)
[
returns a structure of regression statistics
from the maximum likelihood estimation of the reducedform model.h
,pValue
,stat
,cValue
,reg1
]
= lmctest(...)
[
returns a structure of regression statistics
from the OLS estimation of the filtered data on a linear trend.h
,pValue
,stat
,cValue
,reg1
,reg2
]
= lmctest(...)
Input Arguments

Vector of timeseries data. The last element is the most recent observation. The test ignores NaN values, which indicate missing entries. 
NameValue Arguments

Scalar or vector of nominal significance levels for the tests. Set values between 0.01 and 0.1. Default: 

Scalar or vector of nonnegative integers indicating the number For best results, give a suitable value for Default: 

Scalar or vector of Boolean values indicating whether or not
to include the deterministic trend term Determine the value of Default: 

Character vector, such as Default: 
Output Arguments

Vector of Boolean decisions for the tests, with length equal
to the number of tests. Values of 

Vector of pvalues of the test statistics, with length equal to the number of tests. Values are righttail probabilities. When test statistics are outside tabulated critical values,


Vector of test statistics, with length equal to the number of tests. For details, see Test Statistics. 

Vector of critical values for the tests, with length equal to the number of tests. Values are for righttail probabilities. 

Structure of regression statistics from the maximum likelihood estimation of the reducedform model. The structure is described in Regression Statistics Structure. 

Structure of regression statistics The structure is described in Regression Statistics Structure. 
Examples
More About
Algorithms
Test statistics follow nonstandard distributions under the null,
even asymptotically. Asymptotic critical values for a standard set
of significance levels between 0.01 and 0.1, for models with and without
a trend, have been tabulated in [2] using
Monte Carlo simulations. Critical values and pvalues
reported by lmctest
are interpolated from the
tables. Tables are identical to those for kpsstest
.
[1] shows that bootstrapped critical values, used by
tests with a unit root null (such as adftest
and pptest
),
are not possible for lmctest
. As a result, size
distortions for small samples may be significant, especially for highly
persistent processes.
[3] shows that the test is robust when p takes values greater than the value in the datagenerating process. [3] also notes simulation evidence that, under the null, the marginal distribution of the MLE of b_{p} is asymptotically normal, and so may be subject to a standard ttest for significance. Estimated standard errors, however, are unreliable in cases where the MA(1) coefficient a is near 1. As a result, [4] proposes another test for model order, valid under both the null and the alternative, that relies only on the MLEs of b_{p} and a, and not on their standard errors.
References
[1] Caner, M., and L. Kilian. “Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP Debate.“ Journal of International Money and Finance. Vol. 20, 2001, pp. 639–657.
[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] Leybourne, S. J., and B. P. M. McCabe. “A Consistent Test for a Unit Root.” Journal of Business and Economic Statistics. Vol. 12, 1994, pp. 157–166.
[4] Leybourne, S. J., and B. P. M. McCabe. “Modified Stationarity Tests with DataDependent ModelSelection Rules.” Journal of Business and Economic Statistics. Vol. 17, 1999, pp. 264–270.
[5] Schwert, G. W. “Effects of Model Specification on Tests for Unit Roots in Macroeconomic Data.” Journal of Monetary Economics. Vol. 20, 1987, pp. 73–103.