Abstract: This paper proposes a method for predicting the probability density of a variable of interest
in the presence of model ambiguity. In the first step, each candidate parametric model is
estimated minimizing the KullbackLeibler 'distance' (KLD) from a reference nonparametric
density estimate. Given that the KLD represents a measure of uncertainty about the true
structure, in the second step, its information content is used to rank and combine the estimated
models. The paper shows that the KLD between the nonparametric and the parametric density
estimates is asymptotically normally distributed. This result leads to determining the weights
in the model combination, using the distribution function of a Normal centered on the average
performance of all plausible models. Consequently, the final weight is determined by the ability
of a given model to perform better than the average. As such, this combination technique does
not require the true structure to belong to the set of competing models and is computationally
simple. I apply the proposed method to estimate the density function of daily stock returns under
different phases of the business cycle. The results indicate that the double Gamma distribution
is superior to the Gaussian distribution in modeling stock returns, and that the combination
outperforms each individual candidate model both in and outofsample.
Keywords: Density forecast comparison, kernel density estimation, entropy, model combination
Full paper (373 KB PDF)
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Last update: January 28, 2005
