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GaussianLikelihoodAr1#

class GaussianLikelihoodAr1[source]#

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.