GaussianLikelihoodAr1

class GaussianLikelihoodAr1

Gaussian likelihood function with AR1 autocorrelated residuals.

Notes

The Gaussian log-likelihood function with AR1 autocorrelated residual is defined as:

\[\log(L) = -\frac{N-1}{2}\log(2\pi\sigma^2) + \frac{\sum_{i=1}^N - (\epsilon_i - \phi \epsilon_{i-\Delta t})^2} {2\sigma^2}\]

where \(N\) is the number of observations, \(\sigma^2\) is the variance of the residuals, \(\epsilon_i\) is the residual at time \(i\) and \(\mu\) is the mean of the residuals. \(\Delta t\) is the time step between the observations. \(\phi\) is the autoregressive parameter. The parameters \(\phi\) and \(\sigma^2\) need to be estimated.

Methods

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