论文标题
估算随时间变化的内核密度和COVID-19对金融市场的影响的年代学
Estimation of time-varying kernel densities and chronology of the impact of COVID-19 on financial markets
论文作者
论文摘要
随时间变化的内核密度估计取决于两个免费参数：带宽和折现因子。我们建议选择这些参数，以最大程度地减少与概率密度预测验证的传统要求一致的标准。这些要求既是所谓的概率积分变换的统一性和独立性，这些变换是应用于观测值的预测时间变化的累积分布。因此，我们建立了一个新的数值标准，该标准通过改编的Kolmogorov-Smirnov统计量的平均值既包含均匀性和独立性。我们将这种方法应用于Covid-19危机期间的金融市场。我们确定了几个股票指数的每日价格回报的时间变化密度，并使用各种分歧统计数据，我们能够描述危机的时间顺序以及区域差异。例如，我们观察到Covid-19对中国金融市场的影响更大，对美国产生了强烈的影响，并且在欧洲的恢复缓慢。
The time-varying kernel density estimation relies on two free parameters: the bandwidth and the discount factor. We propose to select these parameters so as to minimize a criterion consistent with the traditional requirements of the validation of a probability density forecast. These requirements are both the uniformity and the independence of the so-called probability integral transforms, which are the forecast time-varying cumulated distributions applied to the observations. We thus build a new numerical criterion incorporating both the uniformity and independence properties by the mean of an adapted Kolmogorov-Smirnov statistic. We apply this method to financial markets during the COVID-19 crisis. We determine the time-varying density of daily price returns of several stock indices and, using various divergence statistics, we are able to describe the chronology of the crisis as well as regional disparities. For instance, we observe a more limited impact of COVID-19 on financial markets in China, a strong impact in the US, and a slow recovery in Europe.
