We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. A feature that makes this family particularly desirable for econometric applications is that it possesses closed-form expressions for its anti-derivatives (e.g., the cumulative density function). We illustrate the usefulness of these distributions in two applications. In the first application, we use a scaled and shifted t-distribution to produce density forecasts of U.S. inflation and show that these forecasts are more accurate, out-ofsample, than density forecasts obtained using normal or standard t-distributions. In the second application, we replicate the option-pricing exercise of Abadir and Rockinger (2003) using a mixture of scaled and shifted t-distributions and obtain comparably good results, while gaining analytical tractability. KeywordsARMA-GARCH models, neural networks, nonparametric density estimation, forecast accuracy, option pricing, risk neutral density JEL Classification C63, C53, C45 CommentsThe authors wish to thank
Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may $EVWUDFWThe integration of fuzzy logic systems and neural networks in data driven nonlinear modeling applications has generally been limited to functions based upon the multiplicative fuzzy implication rule for theoretical and computational reasons. We derive a universal approximation result for the minimum fuzzy implication rule as well as a differentiable substitute function that allows fast optimization and function approximation with neuro-fuzzy networks.
In response to the perceived instability of the relations between traditional monetary aggregates and nominal aggregate demand a number of nonstandard indicator variables have been developed to enable monetary policy to respond to, and counteract, incipient inflationary pressures before much inflation has developed. While the Federal Reserve Board is believed to pay increasing attention to such indicator variables, it is unclear which ones are perceived as particularly important. In this note, we present a variation of the monetary impulse measure (MIM), which was recently developed by McCallum and Hargraves (Staff studies for the World Economic Outlook, 1995). Modifying the original specification of the measure, we show that the new MIM's performance in explaining actual Fed decisions is clearly superior to other indicator variables, which are widely believed to guide US monetary policy.
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