GaussianLikelihood

class GaussianLikelihood

Gaussian likelihood function for homoscedastic, uncorrelated errors.

Notes

The Gaussian log-likelihood function [Smith et al., 2015] is defined as:

\[\log(L) = -\frac{N}{2}\log(2\pi\sigma^2) - \frac{\sum_{t=1}^N \epsilon_t^2}{2\sigma^2}\]

where \(N\) is the number of observations, \(\sigma^2\) is the variance of the residuals, and \(\epsilon_t\) is the residual at time \(t\). The parameter \(\sigma^2\) needs to be estimated.

The current implementation is valid for equidistant time series only.

Methods

__init__
compute	Compute the log-likelihood.
get_init_parameters	Get the initial parameters for the log-likelihood function.