具有确定性时变截距的新 GARCH 模型
A new GARCH model with a deterministic time-varying intercept
AI总结：
提出一种在标准 GARCH 模型波动率方程中引入确定性时变截距的新模型，以捕捉金融时间序列的渐变非平稳性，并证明了 QMLE 的渐近性质及该模型对降低波动率持续性的作用。
摘要：
长的金融时间序列通常表现出无条件波动率的渐变。我们提出了一种新模型，以简约的方式捕捉这种非平稳性。该模型通过在标准 GARCH 模型的波动率方程中引入确定性时变截距进行扩展。它能够捕捉缓慢影响时间序列振幅的结构性变化，同时保持短期动态恒定。我们将截距参数化为逻辑过渡函数的线性组合。我们证明，该模型可由波动率的乘法分解推导得出，并保留了方差分解的金融动机。我们利用局部平稳过程理论证明，模型参数的拟最大似然估计量（QMLE）具有一致性和渐近正态分布。我们在一项小规模模拟研究中考察了渐近近似的精度。对 Oracle Corporation 股票收益率的实证应用证明了该模型的实用性。我们发现，在波动率方程中包含时变截距，可降低由 GARCH 参数估计所隐含的持续性。
英文摘要：
It is common for long financial time series to exhibit gradual change in the unconditional volatility. We propose a new model that captures this type of nonstationarity in a parsimonious way. The model augments the volatility equation of a standard GARCH model by a deterministic time-varying intercept. It captures structural change that slowly affects the amplitude of a time series while keeping the short-run dynamics constant. We parameterize the intercept as a linear combination of logistic transition functions. We show that the model can be derived from a multiplicative decomposition of volatility and preserves the financial motivation of variance decomposition. We use the theory of locally stationary processes to show that the quasi maximum likelihood estimator (QMLE) of the parameters of the model is consistent and asymptotically normally distributed. We examine the quality of the asymptotic approximation in a small simulation study. An empirical application to Oracle Corporation stock returns demonstrates the usefulness of the model. We find that the persistence implied by the GARCH parameter estimates is reduced by including a time-varying intercept in the volatility equation.
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