GitHub

Variance from covariance

Statistics.var — Method
Statistics.var(ce::AbstractCovarianceEstimator, X::MatNum; dims::Int = 1, kwargs...)

Compute the variance vector from the diagonal of the covariance matrix.

This method extracts the diagonal of the covariance matrix returned by Statistics.cov(ce, X; dims = dims, kwargs...) and reshapes it into a row or column vector depending on dims.

Mathematical definition

\[\begin{align} \hat{\sigma}_i^2 &= \hat{\mathbf{\Sigma}}_{ii}\,. \end{align}\]

Where:

  • $\hat{\sigma}_i^2$: Variance of asset $i$.
  • $\hat{\mathbf{\Sigma}}$: Estimated covariance matrix.
  • $\hat{\mathbf{\Sigma}}_{ii}$: $i$-th diagonal element of $\hat{\mathbf{\Sigma}}$.

Arguments

  • ce: Covariance estimator.
  • X: Data matrix of asset returns (observations × assets).
  • dims: Dimension along which to perform the computation.
  • kwargs...: Additional keyword arguments passed to the covariance estimator.

Returns

  • var::Matrix{<:Number}: Variance vector, shaped as (1, N) if dims == 1 or (N, 1) if dims == 2.

Related

source
Statistics.std — Method
Statistics.std(ce::AbstractCovarianceEstimator, X::MatNum; dims::Int = 1, kwargs...)

Compute the standard deviation vector from the diagonal of the covariance matrix.

This method extracts the diagonal of the covariance matrix returned by Statistics.cov(ce, X; dims = dims, kwargs...), takes the element-wise square root, and reshapes it into a row or column vector depending on dims.

Mathematical definition

\[\begin{align} \hat{\sigma}_i &= \sqrt{\hat{\mathbf{\Sigma}}_{ii}}\,. \end{align}\]

Where:

  • $\hat{\sigma}_i$: Standard deviation of asset $i$.
  • $\hat{\mathbf{\Sigma}}$: Estimated covariance matrix.
  • $\hat{\mathbf{\Sigma}}_{ii}$: $i$-th diagonal element of $\hat{\mathbf{\Sigma}}$.

Arguments

  • ce: Covariance estimator.
  • X: Data matrix of asset returns (observations × assets).
  • dims: Dimension along which to perform the computation.
  • kwargs...: Additional keyword arguments passed to the covariance estimator.

Returns

  • sd::Matrix{<:Number}: Standard deviation vector, shaped as (1, N) if dims == 1 or (N, 1) if dims == 2.

Related

source