# VoseHQIC

=VoseHQIC(FitObject)

Returns the Hannan-Quinn Information Criterion (HQIC) for goodness of fit of a distribution, time series or copula model fitted to data.

The AIC is used to compare different fitted models against each other. The lower the value of the information criterion, the better the fit.

• FitObject - a valid fitted distribution, time series or copula Fit Object

The HQIC is one of the three information criteria included in ModelRisk for ranking various fitted models against each other, the other ones being Akaike's AIC and Schwarz SIC (they are compared here). The reasoning behind information criteria is that the better model is the one that explains the data well with a minimum number of free parameters. HQIC is defined as follows:

with

• n = number of observations (e.g. data values, frequencies)

• k = number of parameters to be estimated (e.g. the Normal distribution has 2: mu and sigma)

• Lmax = the maximized value of the log-Likelihood for the estimated model (i.e. fit the parameters by MLE and record the natural log of the Likelihood.)

Note that in the ModelRisk distribution, time series and copula fitting windows, the negatives of the information criteria are shown to rank the fitted models by. So in the list shown in the window, a higher number means a better fit.

##### Example

Say you have an array with data named DataSet. To compare the fit of a GBM with a GBMMR time series model we could then create a fit object for each, in cells A1 and A2 respectively:

=VoseTimeGBMFitObject(DataSet)

=VoseTimeGBMMRFitObject(DataSet)

and write in cells B1 and B2:

=VoseHQIC(A1)

=VoseHQIC(A2)

Now as you update the DataSet, the fitted objects and their HQIC are adjusted accordingly. This allows one to easily review the appropriateness of models used, as more accurate or recent data becomes available.

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