The specification of GARCH models with stochastic covariates
研究指出在GARCH(1,1)或EGARCH(1,1)模型中加入随机协变量会隐含约束，可能掩盖协变量的真实作用；以交易量为例，放松约束后发现交易量对解释波动率动态作用有限。
Abstract A number of studies investigate whether various stochastic variables explain changes in return volatility by specifying the variables as covariates in a GARCH(1, 1) or EGARCH(1, 1) model. The authors show that these models impose an implicit constraint that can obscure the true role of the covariates in the analysis. They illustrate the problem by reconsidering the role of contemporaneous trading volume in explaining ARCH effects in daily stock returns. Once the constraint imposed in earlier research is relaxed, it is found that specifying volume as a covariate does little to diminish the importance of lagged squared returns in capturing the dynamics of volatility. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:911–934, 2008