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Duke Economics Working Paper #95-53

Estimation of Continuous Time Models for Stock Returns and Interest Rates

George E. Tauchen
A. R. Gallant


The paper uses and extends the Efficient Method of Moments (EMM) technique to estimate and test continuous time diffusion models for stock returns and interest rates. The EMM technique, developed in previous papers by Gallatn and Tauchen along with various collaborators, is a simulation-based method that uses the score function of an auxiliary model as the criterion to define a generlized method of moments (GMM) objective function. The technique is sufficiently general and computationally tractable to handle multivariate diffusions where the state vector is not completely observed. The application to stock returns finds that a four-factor diffusion model with one observed variable can account for the dynamics of the daily return on the S&P Composite Index, 1927-1987. This finding stands in contrast to previous empirical results indicating that discrete-time stochastic volatility models are incapable of explaining the dynamics of the stock return. The application to interest rates involves fitting a three-factor model ot a weekly, 1962-1995, term structure data setcomoprised sorth of (3 month), medium (12 month), and long (10 year) Treasury rates. The Yield-Factor Model is sharply rejected, though extensions that permit convexities in the local variance function come much closer to fitting the data. While not directly undertaking in the paper, applications involving pricing of derivatives could make use of the estimated diffusion models for stock returns adn interest rates.

JEL: G13

Published in Macroeconomic Dynamics, Vol. 1, No. 1, 1997, pp. 135-168.