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arXiv 2107.06758q-fin.ST
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金融ARCH价格过程的短期稳定性

On the short term stability of financial ARCH price processes

Gilles Zumbach

摘要:

对于许多金融应用程序,重要的是要有可靠和易于处理的模型,为资产和指数的行为,例如在风险评估。一个成功的方法是基于统计过程,它在统计特性和易于计算之间取得了适当的平衡。本文主要研究了二次随机过程的稳定性及其长期行为的理论条件。特别地,方差估计量的权重总和应该为1,并且新息的方差应该为1。利用历史数据,可以计算出已实现的经验创新,并评估其统计特性。对于3 ~ 50年的样本,对于股票指数、商品指数和汇率的样本,经验创新的方差总是显著大于1。这种偏离指向短期的不稳定性,或由于变化的条件而导致的快速适应性。创新的另一个理论条件是具有零均值。这种情况也进行了实证研究,一些时间序列显示出显着偏离零。

英文摘要:

For many financial applications, it is important to have reliable and tractable models for the behavior of assets and indexes, for example in risk evaluation. A successful approach is based on ARCH processes, which strike the right balance between statistical properties and ease of computation. This study focuses on quadratic ARCH processes and the theoretical conditions to have a stable long-term behavior. In particular, the weights for the variance estimators should sum to 1, and the variance of the innovations should be 1. Using historical data, the realized empirical innovations can be computed, and their statistical properties assessed. Using samples of 3 to 5 decades, the variance of the empirical innovations are always significantly above 1, for a sample of stock indexes, commodity indexes and FX rates. This departure points to a short term instability, or to a fast adaptability due to changing conditions. Another theoretical condition on the innovations is to have a zero mean. This condition is also investigated empirically, with some time series showing significant departure from zero.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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