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AR.loglike()

statsmodels.tsa.ar_model.AR.loglike

AR.loglike(params) [source]

The loglikelihood of an AR(p) process

Parameters:

Parameters:	params : array The fitted parameters of the AR model
Returns:	llf : float The loglikelihood evaluated at `params`

params : array

The fitted parameters of the AR model

Returns:

llf : float

The loglikelihood evaluated at params

Notes

Contains constant term. If the model is fit by OLS then this returns the conditonal maximum likelihood.

$\frac{\left(n-p\right)}{2}\left(\log\left(2\pi\right)+\log\left(\sigma^{2}\right)\right)-\frac{1}{\sigma^{2}}\sum_{i}\epsilon_{i}^{2}$

If it is fit by MLE then the (exact) unconditional maximum likelihood is returned.

$-\frac{n}{2}log\left(2\pi\right)-\frac{n}{2}\log\left(\sigma^{2}\right)+\frac{1}{2}\left|V_{p}^{-1}\right|-\frac{1}{2\sigma^{2}}\left(y_{p}-\mu_{p}\right)^{\prime}V_{p}^{-1}\left(y_{p}-\mu_{p}\right)-\frac{1}{2\sigma^{2}}\sum_{t=p+1}^{n}\epsilon_{i}^{2}$

where

$\mu_{p}$ is a (p x 1) vector with each element equal to the mean of the AR process and $\sigma^{2}V_{p}$ is the (p x p) variance-covariance matrix of the first p observations.

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.tsa.ar_model.AR.loglike.html