pastas.solver.likelihood.GaussianLikelihoodAr1

class pastas.solver.likelihood.GaussianLikelihoodAr1

Gaussian likelihood function for homoscedastic, autocorrelated residuals.

Notes

The Gaussian log-likelihood function with AR1 autocorrelated residuals [Smith et al., 2015] is defined as:

\[\begin{split}\\log(L) = -\\frac{N-1}{2}\\log(2\\pi\\sigma^2) - \\frac{\\sum_{t=1}^N(\\epsilon_t - \\phi \\epsilon_{t-\\Delta t})^2} {2\\sigma^2}\end{split}\]

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

The current implementation is valid for equidistant time series only.

property nparam: int

Number of parameters in the log-likelihood function.

Methods

get_init_parameters(→ pandas.DataFrame)	Get initial parameters for the log-likelihood function.
compute(→ float)	Compute the log-likelihood.