Covariance matrix

cov(X) cov(X,Y)

| Financial times series object. |

| Financial times series object. |

`cov`

for financial time series objects is
based on the MATLAB^{®} `cov`

function. See `cov`

in the MATLAB documentation.

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.

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