Testing for an Omitted Multiplicative Long-Term Component in GARCH Models
提出一种拉格朗日乘子统计量，用于检验GARCH模型中是否存在由解释变量驱动的乘法长期成分，适用于混合频率数据，并通过S&P 500数据验证。
We consider the problem of testing for an omitted multiplicative long-term component in GARCH-type models. Under the alternative there is a two-component model with a short-term GARCH component that uctuates around a smoothly time-varying long-term component which is driven by the dynamics of an explanatory variable. We suggest a Lagrange Multiplier statistic for testing the null hypothesis that the variable has no explanatory power. We derive the asymptotic theory for our test statistic and investigate its finite sample properties by Monte-Carlo simulation. Our test also covers the mixed-frequency case in which the returns are observed at a higher frequency than the explanatory variable. The usefulness of our procedure is illustrated by empirical applications to S&P 500 return data.