https://github.com/cgeoga/spectralestimators.jl
Fast likelihoods for time series from spectral densities
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Repository
Fast likelihoods for time series from spectral densities
Basic Info
- Host: GitHub
- Owner: cgeoga
- License: mit
- Language: Julia
- Default Branch: main
- Size: 37.1 KB
Statistics
- Stars: 1
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Metadata Files
README.md
SpectralEstimators.jl
This package provides tools for scalably and accurate evaluating the log-likelihood of a Gaussian time series using its spectral density. It is the software companion to Fast Machine-Precision Spectral Likelihoods for Stationary Time Series.
Demonstration
Here is a very quick demonstration that should get you off the ground and collecting all the digits quickly: ```julia using LinearAlgebra, SpectralEstimators
Write some parametric family of spectral densities you want to fit. Here is a
neat model that I don't mention in the paper, but is fun to play with because
it is smooth at the endpoints but potentially rough at the origin, so the
parameter alpha really directly controls how quickly the ACF decays.
function sdf(w, params) (phi, rho, alpha) = params exp(-(abs(sinpi(w))^alpha)/rho) end
Now for the interface, you create an object called "SpectralModel". You can
choose how to evaluate the tail sequence of your ACF: :asexp for the
asymptotic expansion, that will be faster, or :nufft, which will be less
error-prone to functions coded in such a way that AD doesn't give the right
answer.
model = SpectralEstimators.SDFModel(sdf, # your SDF, see above [0.0], # rough points of the SDF rank=72, # fixed rank for the Whittle correction kerneltailmethod=:nufft)
Now we're ready to build our fast and machine-exact approximation for
FSigmaF^H, as described in the paper. In this example, we build a 3k x 3k
matrix.
parametricsdf = SpectralEstimators.ParametricSDF(model, (5.0, 0.1, 1.25)) fftcov = SpectralEstimators.fftcovmat(parametricsdf, 3_000)
Enjoy! Take a look at the source to see all the methods. Here is a simple case
of the negative log-likelihood (nll):
@show SpectralEstimators.nll(fftcov, rand(3000)) ```
Owner
- Name: Chris Geoga
- Login: cgeoga
- Kind: user
- Location: Madison, WI
- Website: https://chrisgeoga.com
- Repositories: 16
- Profile: https://github.com/cgeoga
Assistant Professor of Statistics at UW Madison
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| Name | Commits | |
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| Chris Geoga | g****a@w****u | 7 |
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