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Leybourne-McCabe stationarity test
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(...)
h = lmctest(y) assesses the null hypothesis that a univariate time series y is a trend stationary AR(p) process, against the alternative that it is a nonstationary ARIMA(p,1,1) process.
h = lmctest(y,'ParameterName',ParameterValue) accepts one or more comma-separated parameter name/value pairs. Specify ParameterName inside single quotes. Perform multiple tests by passing a vector value for any parameter. Multiple tests yield vector results.
[h,pValue] = lmctest(...) returns p-values of the test statistics.
[h,pValue,stat] = lmctest(...) returns the test statistics.
[h,pValue,stat,cValue] = lmctest(...) returns critical values for the tests.
[h,pValue,stat,cValue,reg1] = lmctest(...) returns a structure of regression statistics from the maximum likelihood estimation of the reduced-form model.
[h,pValue,stat,cValue,reg1,reg2] = lmctest(...) returns a structure of regression statistics from the OLS estimation of the filtered data on a linear trend.
y |
Vector of time-series data. The last element is the most recent observation. The test ignores NaN values, which indicate missing entries. |
'alpha' |
Scalar or vector of nominal significance levels for the tests. Set values between 0.01 and 0.1. Default: 0.05 |
'Lags' |
Scalar or vector of nonnegative integers indicating the number p of lagged values of y to include in the structural model (equal to the number p of lagged changes of y in the reduced-form model). For best results, give a suitable value for 'lags'. For information on selecting 'lags', see Determine Appropriate Lags. Default: 0 |
'trend' |
Scalar or vector of Boolean values indicating whether or not to include the deterministic trend term d*t in the structural model (equivalent to including the drift term d in the reduced-form model). Determine the value of trend by the growth characteristics of the time series y. Choose trend with a specific testing strategy in mind. If y is growing, set trend to true to provide a reasonable comparison of a trend-stationary null and a unit-root process with drift. If y does not exhibit long-term growth characteristics, set trend to false. Default: true |
'test' |
String or cell vector of strings indicating which estimate of the variance $${\sigma}_{1}^{2}$$ to use in computing the test statistic. Values are 'var1' or 'var2'. Default: 'var2' |
h |
Vector of Boolean decisions for the tests, with length equal to the number of tests. Values of h equal to 1 indicate rejection of the AR(p) null in favor of the ARIMA(p,1,1) alternative. Values of h equal to 0 indicate a failure to reject the AR(p) null. |
pValue |
Vector of p-values of the test statistics, with length equal to the number of tests. Values are right-tail probabilities. |
stat |
Vector of test statistics, with length equal to the number of tests. For details, see Test Statistics. |
cValue |
Vector of critical values for the tests, with length equal to the number of tests. Values are for right-tail probabilities. |
reg1 |
Structure of regression statistics from the maximum likelihood estimation of the reduced-form model. The structure is described in Regression Statistics Structure. |
reg2 |
Structure of regression statistics The structure is described in Regression Statistics Structure. |
[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 Data-Dependent Model-Selection 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.
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