Stochastic volatility demand systems

ABSTRACT

We address the estimation of stochastic volatility demand systems. In particular, we relax the homoscedasticity assumption and instead assume that the covariance matrix of the errors of demand systems is time-varying. Since most economic and financial time series are nonlinear, we achieve superior modeling using parametric nonlinear demand systems in which the unconditional variance is constant but the conditional variance, like the conditional mean, is also a random variable depending on current and past information. We also prove an important practical result of invariance of the maximum likelihood estimator with respect to the choice of equation eliminated from a singular demand system. An empirical application is provided, using the BEKK specification to model the conditional covariance matrix of the errors of the basic translog demand system.

KEYWORDS:

• Flexible functional forms
• Volatility

JEL CLASSIFICATION:

• C32
• E52
• E44

Acknowledgement

We would like to thank two anonymous referees for comments that greatly improved the article.