INFERENCE ON GARCH-MIDAS MODELS WITHOUT ANY SMALL-ORDER MOMENT
研究了GARCH-MIDAS模型在缺乏小阶矩条件下的统计推断，证明了准最大似然估计的强相合性和渐近正态性，并提出了基于渐近理论和自助法的长期波动率检验，通过蒙特卡洛实验和金融数据验证。
In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real financial data.