com.numericalmethod.suanshu.finance.trading.meanreversion.daspremont2008

Class AhatEstimation

java.lang.Object

com.numericalmethod.suanshu.finance.trading.meanreversion.daspremont2008.AhatEstimation

public class AhatEstimation
extends Object

Estimates the coefficient of a VAR(1) model by penalized maximum likelihood. The vector autoregressive process is: \[ S_{t}=S_{t-1}A+Z_{t} \] \(S_{t}\) is the portfolio process, \(A\) the coefficient matrix, and \(Z_{t}\) a vector of i.i.d. Gaussian noise. The penalized maximum likelihood problem is (eq. 15 in the reference): \[ a_{i}=\arg\min_{x} ||S_{it}-S_{t-1}x||^{2}+\gamma ||x||_{1} \] where \(a_{i}\) is the i-th column of \(A\).

See Also:

"A. d'Aspremont, "eq.2," Identifying Small Mean Reverting Portfolios, 2008."

Constructor Summary

Constructors

Constructor and Description
AhatEstimation(Matrix St, Matrix St_m1, double gamma) Estimates the coefficient matrix of a vector autoregressive process of order 1.

Method Summary

Modifier and Type	Method and Description
Matrix	compute()

Methods inherited from class java.lang.Object

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

Constructor Detail

AhatEstimation

public AhatEstimation(Matrix St,
                      Matrix St_m1,
                      double gamma)

Estimates the coefficient matrix of a vector autoregressive process of order 1.

Parameters:

St - the portfolio price process

St_m1 - the lagged portfolio price process

gamma - the penalty

Method Detail

compute

public Matrix compute()