For non Gaussian models, the Kalman filter is just the best linear
forecasting model and is not the optimal filter. The likelihood estimation
based on the normal distribution should be interpreted as the
quasi-likelihood. In this case, the usual asymptoptic variance based on the
inverse of the hessian will not give the correct result. The QML asymptotic
variance is calculated using the so-called "sandwich" estimator. This can be
estimated in FinMetrics if the model is fit with the SsfFitFast() function
instead of the SsfFit() function. (see section 14.4.3 in the 2nd Edition of
Modeling Financial Time Series for an example based on estimating a
stochastic volatility model. You have to update the FM 2.0 module to get the
updated version of my book). The QML sandwhich variance can be computed by
calling the summary() function with the optional argument method="qmle" or
by calling the vcov() extractor function with optional argument
method="qmle".
-----Original Message-----
From: s-news-owner@lists.biostat.wustl.edu
[mailto:s-news-owner@lists.biostat.wustl.edu] On Behalf Of James Dartnall
Sent: Tuesday, January 24, 2006 11:56 AM
To: S-Plus list
Subject: [S] calculating the hessian in a non-Gauss ssf
Dear all,
The new routine that calculates the hessian and "vcov" built in to the
Finmetrics 2 function SsfFit is very useful for calculating the standard
errors on hyperparameters in Gaussian state space models. Is there any
function that anyone knows of that will calculate the hessian for the
hyperparameters on Gaussian states within a non-Gaussian model such as say a
Poisson model but with a Gaussian local level trend? Presumably this
function would be passed to the hessian argument in nlminb but I'm not sure.
I'm using S-Plus 7 and Finmetrics 2.
Thanks for any advice
James Dartnall
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