dev.nm.stat.covariance

Class LedoitWolf2004

java.lang.Object

dev.nm.stat.covariance.LedoitWolf2004

public class LedoitWolf2004
extends Object

To estimate the covariance matrix, Ledoit and Wolf (2004) suggests using the matrix obtained from the sample covariance matrix through a transformation called shrinkage. This tends to pull the most extreme coefficients towards more central values, thereby systematically reducing estimation error where it matters most. Statistically, the challenge is to know the optimal shrinkage intensity, and they also give the formula for that. Note: The input matrix here is T-by-N, while the description in the referenced paper assumes the matrix of stock returns is N-by-T.

See Also:

• "Olivier Ledoit and Michael Wolf, "Honey, I Shrunk the Sample Covariance Matrix," in Journal of Portfolio Management, Volume 31, Number 1, 2004."
• "Olivier Ledoit and Michael Wolf, "Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection," in Journal of Empirical Finance, Volume 10, Issue 5, December 2003, pages 603-621."

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	LedoitWolf2004.Result The estimator and some intermediate values computed by the algorithm.

Constructor Summary

Constructors

Constructor and Description
LedoitWolf2004() Creates the algorithm instance, using an unbiased sample covariance matrix by default.
LedoitWolf2004(boolean unbiased) Creates the algorithm instance, with the option to use an unbiased or biased sample covariance matrix.

Method Summary

Modifier and Type	Method and Description
LedoitWolf2004.Result	compute(Matrix Y) Estimates the covariance matrix for a given matrix Y (each column in Y is a time-series), with the optimal shrinkage parameter computed by the algorithm.
LedoitWolf2004.Result	compute(Matrix Y, double shrinkage) Estimates the covariance matrix for a given matrix Y (each column in Y is a time-series), with the given shrinkage parameter.

Methods inherited from class java.lang.Object

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

Constructor Detail

LedoitWolf2004

public LedoitWolf2004()

Creates the algorithm instance, using an unbiased sample covariance matrix by default.

LedoitWolf2004

public LedoitWolf2004(boolean unbiased)

Creates the algorithm instance, with the option to use an unbiased or biased sample covariance matrix.

Parameters:

unbiased - true to use unbiased covariance matrix

Method Detail

compute

public LedoitWolf2004.Result compute(Matrix Y)

Estimates the covariance matrix for a given matrix Y (each column in Y is a time-series), with the optimal shrinkage parameter computed by the algorithm.

Parameters:

Y - the input matrix

Returns:

the estimator

compute

public LedoitWolf2004.Result compute(Matrix Y,
                                     double shrinkage)

Estimates the covariance matrix for a given matrix Y (each column in Y is a time-series), with the given shrinkage parameter.

Parameters:

Y - the input matrix

shrinkage - the shrinkage parameter

Returns:

the estimator