cointegration test_covariance stationary_对Johansen test的理解

[h,pValue,stat,cValue,reg1,reg2]= egcitest(Y)

[h,pValue,stat,cValue,reg1,reg2]= egcitest(Y,Name,Value)

Engle-Granger tests assess the null hypothesis of no cointegrationamong the time series in Y. The test regresses Y(:,1) on Y(:,2:end),then tests the residuals for a unit root.

[,,,,,]= egcitest() performs the Engle-Grangertest on a data matrix Y.

[,,,,,]= egcitest(,) performsthe Engle-Granger test on a data matrix Y withadditional options specified by one or more Name,Value pairarguments.

numObs-by-numDims matrixrepresenting numObs observations of a numDims-dimensionaltime series y(t),with the last observation the most recent. Y cannothave more than 12 columns. Observations containing NaN valuesare removed.

Specify optional comma-separated pairs of Name,Value arguments.Name is the argumentname and Value is the correspondingvalue. Name must appearinside single quotes (' ').You can specify several name and value pairarguments in any order as Name1,Value1,...,NameN,ValueN.

Vector or cell vector of vectors containing coefficients [a;b]to be held fixed in the cointegrating regression. The length of a is0, 1, 2 or 3, depending on , with coefficientorder: constant, linear trend, quadratic trend. The length of b is numDims1. It is assumed that the coefficientof y1 = Y(:,1) hasbeen normalized to 1. NaN values indicate coefficientsto be estimated. If cvec is completely specified(no NaN values), no cointegrating regression isperformed.

Default: Completely unspecified cointegrating vector (all NaN values).

Character vector, such as 'ADF', or cellvector of character vectors indicating the form of the residual regression.

Values are:

'ADF' augmented Dickey-Fullertest of residuals from the cointegrating regression

'PP' Phillips-Perron test

Test statistics are computed by calling adftest and pptest with the model parameter set to 'AR',assuming data have been demeaned or detrended, as necessary, in thecointegrating regression.

Default: 'ADF'

Character vector, such as 't1', or cell vectorof character vectors indicating the type of test statistic computedfrom the residual regression.

Values are:

't1' a " test"

't2' a "z test"

The meaning of the parameter depends on the value of (seethe documentation for the test parameter in adftest and pptest).

Default: t1

Scalar or vector of nominal significance levels for the tests.Values must be between 0.001 and 0.999.

Default: 0.05

Single-element parameter values are expanded to the length ofany vector value (the number of tests). Vector values must have equallength. If any value is a row vector, all outputs are row vectors.

Vector of Boolean decisions for the tests, with length equalto the number of tests. Values of h equal to 1 (true)indicate rejection of the null in favor of the alternative of cointegration.Values of h equal to 0 (false)indicate a failure to reject the null.

Vector of critical values for the tests, with length equal tothe number of tests. Values are for left-tail probabilities. Sinceresiduals are estimated rather than observed, critical values aredifferent from those used in adftest or pptest (unless the cointegrating vectoris completely specified by ). egcitest loadstables of critical values from the file Data_EGCITest.mat,then linearly interpolates test values from the tables. Critical valuesin the tables were computed using methods described in .

A suitable value for must be determinedin order to draw valid inferences from the test. See notes on the lags parameterin the documentation for adftest and pptest.

Samples with less than ~20 to 40 observations (depending onthe dimension of the data) can yield unreliable critical values, andso unreliable inferences. See .

If cointegration is inferred, residuals from the outputcan be used as data for the error-correction term in a VEC representationof y(t).See . Estimation of autoregressivemodel components can then be performed with estimate, treatingthe residual series as exogenous.

[1] Engle, R. F. and C. W. J. Granger. "Co-Integrationand Error-Correction: Representation, Estimation, and Testing." Econometrica.v. 55, 1987, pp. 251276.

[2] Hamilton, J. D. Time SeriesAnalysis. Princeton, NJ: Princeton University Press, 1994.

[3] MacKinnon, J. G. "Numerical DistributionFunctions for Unit Root and Cointegration Tests." Journalof Applied Econometrics. v. 11, 1996, pp. 601618.

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