Stochastic volatility demand systems
提出一种估计随机波动需求系统的方法，放松了同方差假设，允许误差协方差矩阵随时间变化，并证明了最大似然估计量在奇异需求系统中对方程选择的不变性，最后用BEKK模型对基本超越对数需求系统进行了实证应用。
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.