com.numericalmethod.suanshu.stats.cointegration

Class CointegrationMLE

java.lang.Object

com.numericalmethod.suanshu.stats.cointegration.CointegrationMLE

All Implemented Interfaces:

java.io.Serializable

public class CointegrationMLE
extends java.lang.Object
implements java.io.Serializable

Two or more time series are cointegrated if they each share a common type of stochastic drift, that is, to a limited degree they share a certain type of behavior in terms of their long-term fluctuations, but they do not necessarily move together and may be otherwise unrelated. If two or more series are individually integrated (in the time series sense) but some linear combination of them has a lower order of integration, then the series are said to be cointegrated. A common example is where the individual series are first-order integrated (I(1)) but some (cointegrating) vector of coefficients exists to form a stationary linear combination of them.

This implementation to estimate the cointegrating factors is the Johansen method, named after Søren Johansen. It is an MLE (maximum likelihood estimation) method. The Johansen test is a procedure for testing cointegration of several I(1) time series using MLE. This test permits more than one cointegrating relationship. It is more generally applicable than the Engle–Granger test.

See Also:

• Søren Johansen, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press, USA. February 1, 1996.
• Kevin Sun, Notes on Cointegration, February 23, 2011.
• Wikipedia: Cointegration
• Wikipedia: Johansen test

, Serialized Form

Constructor Summary

Constructors

Constructor and Description
CointegrationMLE(SimpleMultiVariateTimeSeries ts, boolean intercept) Perform the Johansen MLE procedure on a multivariate time series, using the EIGEN test, with the number of lags = 2.
CointegrationMLE(SimpleMultiVariateTimeSeries ts, boolean intercept, int p) Perform the Johansen MLE procedure on a multivariate time series, using the EIGEN test.
CointegrationMLE(SimpleMultiVariateTimeSeries ts, boolean intercept, int p, Matrix D) Perform the Johansen MLE procedure on a multivariate time series.

Method Summary

Modifier and Type	Method and Description
ImmutableMatrix	alpha() Get the set of adjusting coefficients, by columns.
ImmutableMatrix	beta() Get the set of cointegrating factors, by columns.
ImmutableVector	beta(int r) Get the r-th cointegrating factor, counting from 1.
ImmutableVector	getEigenvalues() Get the set of real eigenvalues.
int	n() Get the number of rows of the multivariate time series used in regression.
int	rank() Get the rank of the system, i.e., the number of (real) eigenvalues.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

CointegrationMLE

public CointegrationMLE(SimpleMultiVariateTimeSeries ts,
                        boolean intercept,
                        int p,
                        Matrix D)

Perform the Johansen MLE procedure on a multivariate time series.

Parameters:

ts - a multivariate time series

intercept - indicate whether an intercept is included in the estimation

p - the number of lags, e.g., 2

D - the exogenous factor matrix (excluding the intercept)

CointegrationMLE

public CointegrationMLE(SimpleMultiVariateTimeSeries ts,
                        boolean intercept,
                        int p)

Perform the Johansen MLE procedure on a multivariate time series, using the EIGEN test.

Parameters:

ts - a multivariate time series

intercept - indicate whether an intercept is included in the estimation

p - the number of lags, e.g., 2

CointegrationMLE

public CointegrationMLE(SimpleMultiVariateTimeSeries ts,
                        boolean intercept)

Perform the Johansen MLE procedure on a multivariate time series, using the EIGEN test, with the number of lags = 2.

Parameters:

ts - a multivariate time series

intercept - indicate whether an intercept is included in the estimation

Method Detail

alpha

public ImmutableMatrix alpha()

Get the set of adjusting coefficients, by columns.

Returns:

α, the adjusting coefficients

beta

public ImmutableMatrix beta()

Get the set of cointegrating factors, by columns.

Returns:

β, the cointegrating factors

beta

public ImmutableVector beta(int r)

Get the r-th cointegrating factor, counting from 1.

Parameters:

r - an index

Returns:

β_r, the r-th cointegrating factor

getEigenvalues

public ImmutableVector getEigenvalues()

Get the set of real eigenvalues.

Returns:

the real eigenvalues

rank

public int rank()

Get the rank of the system, i.e., the number of (real) eigenvalues.

Returns:

the rank

n

public int n()

Get the number of rows of the multivariate time series used in regression.

Returns:

ts.size - p