Debiased Whittle likelihood

DebiasedWhittleLikelihood(model::Type{<:TimeSeriesModel}, ts, Δ; lowerΩcutoff, upperΩcutoff, taper)
DebiasedWhittleLikelihood(model::Type{<:TimeSeriesModel}, timeseries::TimeSeries; lowerΩcutoff, upperΩcutoff, taper)

Generate a function to evaluate the Debiased Whittle likelihood it's gradient and expected Hessian.

Create a callable struct which prealloctes memory appropriately.

(f::DebiasedWhittleLikelihood)(θ)

Evaluates the Whittle likelihood at θ.

(f::DebiasedWhittleLikelihood)(F,G,EH,θ)

Evaluates the Whittle likelihood at θ and stores the gradient and expected Hessian in G and EH respectively. If F, G or EH equal nothing, then the function, gradient or expected Hessian are not evaluated repsectively.

Aruguments

• model: the model for the process. Should be of type TimeSeriesModel, so OU and not OU(1,1).
• ts: the timeseries in the form of an n by d matrix (where d is the dimension of the time series model).
• Δ: the sampling rate of the time series.
• timeseries: can be provided instead of ts and Δ. Must be of type TimeSeries.
• lowerΩcutoff: the lower bound of the frequency range included in the likelihood.
• upperΩcutoff: the upper bound of the frequency range included in the likelihood.
• taper: optional taper which should be a vector of length size(ts,1), or nothing in which case no taper will be used.

Note that to use the gradient the model must have grad_add_sdf! or grad_acv! specified. Similarly, to use the Hessian, the model must have hess_add_sdf! or hess_acv! specified.

Examples

julia> obj = DebiasedWhittleLikelihood(OU, ones(1000), 1)
Debiased Whittle likelihood for the OU model.

julia> obj([1.0, 1.0])
-1982.0676530999626

julia> F, G, EH = 0.0, zeros(2), zeros(2,2)
(0.0, [0.0, 0.0], [0.0 0.0; 0.0 0.0])

julia> obj(F, G, EH, [1.0, 1.0])
-1982.0676530999626

julia> G
2-element Vector{Float64}:
 1998.3136810970122
 -685.7904154568779

julia> H
2×2 Matrix{Float64}:
 -0.00967179   0.0607696
  0.0607696   -0.381827