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Windowed variance

PortfolioOptimisers.WindowedVariance — Type
struct WindowedVariance{__T_ve, __T_w, __T_window} <: AbstractVarianceEstimator

Variance estimator that restricts computation to a rolling or indexed observation window.

WindowedVariance wraps another variance estimator and applies it to a subset of observations defined by a window and/or custom observation weights. This enables time-varying or recency-weighted variance estimation.

Fields

  • ve: Variance estimator.

  • w: Optional observation weights vector observations × 1, or a concrete subtype of DynamicAbstractWeights. If nothing, the computation is unweighted.

  • window: Observation window. An integer selects the last window observations, and a vector of indices selects those observations.

Constructors

WindowedVariance(;    ve::AbstractVarianceEstimator = SimpleVariance(),    w::Option{<:ObsWeights} = nothing,    window::Option{<:Int_VecInt} = nothing) -> WindowedVariance

Keywords correspond to the struct's fields.

Validation

  • If w is not nothing, !isempty(w).
  • If window is provided, it must be nonempty, nonnegative, and finite.

Propagated parameters

When factory is called on this type, the following @fprop-tagged fields are automatically propagated:

View parameters

When port_opt_view is called on this type, the following @vprop-tagged fields are automatically subset to the selected indices:

Observation weight parameters

When obs_weights_view is called on this type, the following fields are automatically indexed to the selected observations:

Examples

julia> WindowedVariance()WindowedVariance      ve ┼ SimpleVariance         │          me ┼ SimpleExpectedReturns         │             │   w ┴ nothing         │           w ┼ nothing         │   corrected ┴ Bool: true       w ┼ nothing  window ┴ nothing

Related

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Statistics.var — Method
Statistics.var(ve::WindowedVariance, X::MatNum; dims::Int = 1, mean = nothing, iv::Option{<:MatNum} = nothing, kwargs...)

Compute Statistics.var over a rolling or indexed observation window (matrix input).

This method selects a window of observations from X (and applies observation weights if specified), then delegates to the underlying variance estimator.

Algorithm

  1. Resolve the window and the observation weights with windowed_preamble, giving inner, a copy of ve.ve that carries the windowed weights, together with the windowed X and the windowed iv.
  2. Call Statistics.var on inner and the windowed X, and return its result. The inner estimator alone decides the value, so the window and the weights are the whole of this method's contribution.

Arguments

  • ve: Windowed variance estimator.
  • X: Data matrix of asset returns (observations × assets).
  • dims: Dimension along which to perform the computation.
  • mean: Optional pre-computed mean passed to the underlying estimator.
  • iv: Optional implied volatility matrix. Used if any internal covariance estimator is an instance of ImpliedVolatility.
  • kwargs...: Additional keyword arguments passed to the underlying estimator.

Returns

  • vr::ArrNum: Variance vector of X, reshaped to be consistent with the dimension along which the value is computed.

Related

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Statistics.var — Method
Statistics.var(ve::WindowedVariance, X::VecNum; mean = nothing)

Compute Statistics.var over a rolling or indexed observation window (vector input).

This method selects a window of observations from X (and applies observation weights if specified), then delegates to the underlying variance estimator.

Algorithm

  1. Resolve the window and the observation weights with windowed_preamble, giving inner, a copy of ve.ve that carries the windowed weights, together with the windowed X.
  2. Call Statistics.var on inner and the windowed X, and return its result. The inner estimator alone decides the value, so the window and the weights are the whole of this method's contribution.

Arguments

  • ve: Windowed variance estimator.
  • X: Data vector of returns.
  • mean: Optional pre-computed mean passed to the underlying estimator.

Returns

  • vr::Number: Variance of X.

Related

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Statistics.std — Method
Statistics.std(ve::WindowedVariance, X::MatNum; dims::Int = 1, mean = nothing, iv::Option{<:MatNum} = nothing, kwargs...)

Compute Statistics.std over a rolling or indexed observation window (matrix input).

This method selects a window of observations from X (and applies observation weights if specified), then delegates to the underlying variance estimator.

Algorithm

  1. Resolve the window and the observation weights with windowed_preamble, giving inner, a copy of ve.ve that carries the windowed weights, together with the windowed X and the windowed iv.
  2. Call Statistics.std on inner and the windowed X, and return its result. The inner estimator alone decides the value, so the window and the weights are the whole of this method's contribution.

Arguments

  • ve: Windowed variance estimator.
  • X: Data matrix of asset returns (observations × assets).
  • dims: Dimension along which to perform the computation.
  • mean: Optional pre-computed mean passed to the underlying estimator.
  • iv: Optional implied volatility matrix. Used if any internal covariance estimator is an instance of ImpliedVolatility.
  • kwargs...: Additional keyword arguments passed to the underlying estimator.

Returns

  • sd::ArrNum: Standard deviation vector of X, reshaped to be consistent with the dimension along which the value is computed.

Related

source
Statistics.std — Method
Statistics.std(ve::WindowedVariance, X::VecNum; mean = nothing)

Compute Statistics.std over a rolling or indexed observation window (vector input).

This method selects a window of observations from X (and applies observation weights if specified), then delegates to the underlying variance estimator.

Algorithm

  1. Resolve the window and the observation weights with windowed_preamble, giving inner, a copy of ve.ve that carries the windowed weights, together with the windowed X.
  2. Call Statistics.std on inner and the windowed X, and return its result. The inner estimator alone decides the value, so the window and the weights are the whole of this method's contribution.

Arguments

  • ve: Windowed variance estimator.
  • X: Data vector of returns.
  • mean: Optional pre-computed mean passed to the underlying estimator.

Returns

  • sd::Number: Standard deviation of X.

Related

source