Volatility Estimation When the Zero-Process is Nonstationary
针对金融收益率中零值分布非平稳导致标准波动率估计失效的问题，提出一种能容纳非平稳零过程的GARCH模型及零调整QMLE估计量，证明其渐近性质，并通过模拟和实证展示其优势。
Financial returns are frequently nonstationary due to the nonstationary distribution of zeros. In daily stock returns, for example, the nonstationarity can be due to an upwards trend in liquidity over time, which may lead to a downwards trend in the zero-probability. In intraday returns, the zero-probability may be periodic: It is lower in periods where the opening hours of the main financial centers overlap, and higher otherwise. A nonstationary zero-process invalidates standard estimators of volatility models, since they rely on the assumption that returns are strictly stationary. We propose a GARCH model that accommodates a nonstationary zero-process, derive a zero-adjusted QMLE for the parameters of the model, and prove its consistency and asymptotic normality under mild assumptions. The volatility specification in our model can contain higher order ARCH and GARCH terms, and past zero-indicators as covariates. Simulations verify the asymptotic properties in finite samples, and show that the standard estimator is biased. An empirical study of daily and intradaily returns illustrate our results. They show how a nonstationary zero-process induces time-varying parameters in the conditional variance representation, and that the distribution of zero returns can have a strong impact on volatility predictions.