# Ledoit-Wolf Shrinkage Variance Estimate

### Description

Returns a variance matrix that shrinks towards the equal correlation matrix – a Ledoit-Wolf estimate.

### Usage

1 2 3 |

### Arguments

`x` |
required.
A numeric matrix.
The rows are observations and the columns are the variables.
In finance, this will be a matrix of returns where the rows are
times and the columns are assets.
For the default value of |

`weights` |
a numeric vector giving the observation weights, or Equal weights can be specified with Otherwise, this must be a
vector of non-negative numbers that is as long as the number
of observations (rows of |

`shrink` |
either |

`center` |
either a single logical value, or a numeric vector as long as
the number of columns of |

`vol.shrink` |
a number between zero and one (inclusive) that says how much to shrink the standard deviations towards the mean standard deviation. |

`sd.min` |
a single integer giving the minimum number of observations needed
in a column of |

`quan.sd` |
a single number in the range of zero to one (inclusive) that says what quantile of the (used) standard deviations to use as the estimate of standard deviation for columns without enough (or any) data. |

`tol` |
a single number indicating how large the smallest eigenvalues
of the answer should be.
All eigenvalues are made to be no smaller than |

`compatible` |
a logical value.
If |

`verbose` |
a number indicating the level of warning messages desired. This currently controls only one warning: If at least 1, then a warning will be issued if all the values
in |

### Value

an estimate of the variance matrix of `x`

.
The sample variance is shrunk towards equal correlation.

This has two additional attributes:

`shrink ` |
the estimated or input amount of shrinkage towards the equal correlation matrix from the sample variance. |

`timedate ` |
the date and time at which the computation was done. |

### Details

Time weights are quite helpful for estimating variances from returns. The default weighting seems to perform reasonably well over a range of situations. However, time weighting was not studied for this estimator.

### Warning

The default value for `weights`

assumes that the last row is the most
recent observation and the first observation is the most ancient observation.

### Research Issues

The method of handling missing values used in the function has not been studied (at all).

The method of boosting the result away from singularity is completely unstudied. For optimization it is wise to move away from singularity, just how to do that best seems like a research question. The method used boosts the smallest eigenvalues, it might be better to increase the diagonal.

### Revision

This help was last revised 2014 March 09.

### Author(s)

Burns Statistics

### References

Olivier Ledoit and Michael Wolf (2004) "Honey, I shrunk the sample covariance matrix". The Journal of Portfolio Management, volume 30, number 4.

### See Also

`factor.model.stat`

, `cov.wt`

,
`slideWeight`

.

### Examples

1 2 3 4 5 6 | ```
## Not run:
var1 <- var.shrink.eqcor(return.matrix)
var.unweighted <- var.shrink.eqcor(return.matrix, weights=1)
## End(Not run)
``` |