WhittleLikelihoodInference
A julia package for Whittle and debiased Whittle likelihood inference. Provides the following functionality:
- Simulating Gaussian processes with a given autocovariance.
- Computation of the (negative) Whittle likelihood, its gradient and its Hessian (including with an arbitrary taper).
- Computation of the (negative) debiased Whittle likelihood, its gradient and its Hessian (including with an arbitrary taper).
- Support for reverse-mode automatic differentiation via ChainRules.jl.
- A fit function which uses solvers from Optim.jl with the option to use dpss tapers from DSP.jl.
- Plotting recipes for second-order properties of interest, including the spectral density function and autocovariance.
- Approximation of the autocovariance from the spectral density function (and for gradients and Hessians).
- Example models including 1D OU and 1D Matern, 2D correlated OU process and arbitrary dimensional Matern.
- Basic non-parametric estimators including the periodogram and Bartlett's method with plotting recipes.
References
Sykulski, A.M., Olhede, S.C., Guillaumin, A.P., Lilly, J.M., Early, J.J. (2019). The debiased Whittle likelihood. Biometrika 106 (2), 251–266.
Grainger, J. P., Sykulski, A. M., Jonathan, P., and Ewans, K. (2021). Estimating the parameters of ocean wave spectra. Ocean Engineering, 229:108934.