摘要翻译：
我们发展了一个统一的检验方法来检测和定年严格平稳的GARCH$(r，s)$（广义自回归条件异方差）过程的爆炸行为。也就是说，我们用一个参数变化的“异常”周期来检验具有常数参数的全局稳定GARCH过程的零假设。在此期间，这种变化可能导致波动过程的爆炸性行为。假定突变的幅度和时间都是未知的。我们发展了一个双最大的测试存在一个中断，然后提供了一个算法来识别变化的周期。我们的理论结果在GARCH过程创新的温和时刻假设下成立。从技术上讲，GARCH模型中QMLE的现有性质需要重新研究，以便在所有可能的变化周期中保持一致。关键结果涉及估计参数的一致弱Bahadur表示，这导致检验统计量弱收敛到高斯过程的最高值。在模拟中，我们表明，该检验具有良好的规模和功率，合理地大的时间序列长度。我们将测试应用于苹果资产回报和比特币回报。
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英文标题：
《A supreme test for periodic explosive GARCH》
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作者：
Stefan Richter, Weining Wang, Wei Biao Wu
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最新提交年份：
2018
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH$(r,s)$ (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against an alternative where there is an 'abnormal' period with changed parameter values. During this period, the change may lead to an explosive behavior of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double supreme test for the existence of a break, and then provide an algorithm to identify the period of change. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the QMLE in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian Process. In simulations we show that the test has good size and power for reasonably large time series lengths. We apply the test to Apple asset returns and Bitcoin returns.
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PDF链接：
https://arxiv.org/pdf/1812.03475