# Documentation

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# cov

Covariance matrix

## Syntax

```cov(X)
cov(X,Y)
```

## Arguments

 `X` Financial times series object. `Y` Financial times series object.

## Description

`cov` for financial time series objects is based on the MATLAB® `cov` function. See `cov`.

If `X` is a financial time series object with one series, `cov(X)` returns the variance. For a financial time series object containing multiple series, where each row is an observation, and each series a variable, `cov(X)` is the covariance matrix.

`diag(cov(X))` is a vector of variances for each series and `sqrt(diag(cov(X)))` is a vector of standard deviations.

`cov(X, Y)`, where `X` and `Y` are financial time series objects with the same number of elements, is equivalent to `cov([X(:) Y(:)])`.

`cov(X)` or `cov(X, Y)` normalizes by (`N` -`1`) if `N` > `1`, where `N` is the number of observations. This makes `cov(X)` the best unbiased estimate of the covariance matrix if the observations are from a normal distribution. For `N` = `1`, `cov` normalizes by `N`.

`cov(X, 1)` or `cov(X, Y, 1)` normalizes by `N` and produces the second moment matrix of the observations about their mean. `cov(X, Y, 0)` is the same as `cov(X, Y)` and `cov(X, 0)` is the same as `cov(X)`. The mean is removed from each column before calculating the result.

## Examples

collapse all

This example shows how to create a covariance matrix for the following dates.

```dates = {'01-Jan-2007';'02-Jan-2007';'03-Jan-2007'}; A = [-1 1 2 ; -2 3 1 ; 4 0 3]; f = fints(dates, A); c = cov(f)```
```c = 10.3333 -4.1667 3.0000 -4.1667 2.3333 -1.5000 3.0000 -1.5000 1.0000 ```