arch.univariate.Normal.loglikelihood¶
-
Normal.loglikelihood(parameters: Sequence[float] | ndarray | Series, resids: ndarray | DataFrame | Series, sigma2: ndarray | DataFrame | Series, individual: bool =
False
) float | ndarray [source]¶ Computes the log-likelihood of assuming residuals are normally distributed, conditional on the variance
- Parameters:¶
- parameters: Sequence[float] | ndarray | Series¶
The normal likelihood has no shape parameters. Empty since the standard normal has no shape parameters.
- resids: ndarray | DataFrame | Series¶
The residuals to use in the log-likelihood calculation
- sigma2: ndarray | DataFrame | Series¶
Conditional variances of resids
- individual: bool =
False
¶ Flag indicating whether to return the vector of individual log likelihoods (True) or the sum (False)
- Returns:¶
ll – The log-likelihood
- Return type:¶
Notes
The log-likelihood of a single data point x is
\[\ln f\left(x\right)=-\frac{1}{2}\left(\ln2\pi+\ln\sigma^{2} +\frac{x^{2}}{\sigma^{2}}\right)\]