Class VECM
- java.lang.Object
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- dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma.VECM
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- Direct Known Subclasses:
VECMLongrun,VECMTransitory
public class VECM extends Object
A Vector Error Correction Model (VECM(p)) has one of the following specifications: Transitory: \[ \Delta Y_t = \mu + \Pi Y_{t-1} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] or Long-run: \[ \Delta Y_t = \mu + \Pi Y_{t-p} + \sum \left ( \Gamma_i Y_{t-1} \right ) + \Psi D_t + \epsilon_t, i = 1, 2, ..., p-1 \] Yt, μ and εt are n-dimensional vectors. The impact matrix Π and the coefficients {Γi} of the lagged time series are n-by-n matrices; Dt is an m-by-1 vector which contains all exogenous variables at time t (excluding the intercept term), and its coefficients are represented by a n-by-m matrix ψ.- See Also:
- S. Johansen, "ch. 3-6, pp. 34-103," Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford, Oxford University Press, 1995.
- S. Johansen, "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, vol. 59, 1551-1580, 1991.
- A. Banerjee et al., Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data, Oxford, Oxford University Press, 1993.
- Wikipedia: Error correction model
- Wikipedia: Johansen test
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description intdimension()Get the dimension of the multivariate time series.ImmutableMatrix[]gamma()Get the AR coefficients of the lagged differences;nullif p = 1ImmutableMatrixgamma(int i)Get the AR coefficient of the i-th lagged differences.ImmutableVectormu()Get the intercept vector.intp()Get the order of the VECM model.ImmutableMatrixpi()Get the impact matrix.ImmutableMatrixpsi()Get the coefficients of the deterministic terms.ImmutableMatrixsigma()Get the white noise covariance matrix.
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Constructor Detail
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VECM
public VECM(Vector mu, Matrix pi, Matrix[] gamma, Matrix psi, Matrix sigma)
Construct a VECM(p) model.- Parameters:
mu- the intercept (constant) vectorpi- the impact matrixgamma- the AR coefficients of the lagged differences;nullif p = 1psi- the coefficients of the deterministic terms (excluding the intercept term)sigma- the white noise covariance matrix
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VECM
public VECM(VECM that)
Copy constructor.- Parameters:
that- a VECM model
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Method Detail
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mu
public ImmutableVector mu()
Get the intercept vector.- Returns:
- the intercept (constant) vector
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pi
public ImmutableMatrix pi()
Get the impact matrix.- Returns:
- the impact matrix
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gamma
public ImmutableMatrix gamma(int i)
Get the AR coefficient of the i-th lagged differences.- Parameters:
i- an index, counting from 1- Returns:
- the AR coefficient of the i-th lagged differences
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gamma
public ImmutableMatrix[] gamma()
Get the AR coefficients of the lagged differences;nullif p = 1- Returns:
- the AR coefficients of the lagged differences;
nullif p = 1
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psi
public ImmutableMatrix psi()
Get the coefficients of the deterministic terms.- Returns:
- the coefficients of the deterministic terms; could be
null
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sigma
public ImmutableMatrix sigma()
Get the white noise covariance matrix.- Returns:
- the white noise covariance matrix
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dimension
public int dimension()
Get the dimension of the multivariate time series.- Returns:
- the dimension of the multivariate time series
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p
public int p()
Get the order of the VECM model.- Returns:
- the order of the VECM model
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