Specification Analysis of Continuous Time Models in Finance

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.