Copyrights to papers in the Duke Economics Working Paper Archive remain with the authors or their assignees. Archive users may download papers and produce them for their own personal use, but downloading of papers for any other activity, including reposting to other electronic bulletin boards or archives, may not be done without the written consent of the authors. It is the authors' responsibility to notify the archive managers when they wish to have the paper removed.

Duke Economics Working Paper #95-49

Specification Analysis of Continuous Time Models in Finance

A. Ronald Galant
George E. Tauchen


The paper describes the use of the Gallant-Tauchen efficient method of moments (EMM) technique for diagnostic checking of stochastic differential equations (SDEs) estimated from financial market data. The EMM technique is a simulation-based method that uses the score function of an auxiliary model as the criterion to define a generalized method of moments (GMM) objective function. The technique can handle multivariate SDEs where the state vector is not completely observed. The optimized GMM objective function is distributed as chi-square and may be used to test model adequacy. Elements of the score function correspond to specific parameters and large values reflect features of data that a rejected SDE specification does not describe well. The diagnostics are illustrated by estimating a three-factor model to weekly, 1962-1995, term structure data comprised of short (3 month), medium (12 month), and long (10 year) Treasury rates. The Yield-Factor Model is sharply rejected, although an extension that permits the local variance function to be a convex function of the interest rates comes much closer to describing the data.

JEL: G13

Published in Modelling Stock Market Volatility: Bridging the Gap to Continuous Time, Peter E. Rossi (ed.), Academic Press, 1996, pp. 357-383.