Estimation of time-varying kernel densities and chronology of the impact of COVID-19 on financial markets

TL;DR

This paper introduces a method for selecting parameters in time-varying kernel density estimation to better understand COVID-19's impact on financial markets, revealing regional disparities and crisis chronology.

Contribution

It proposes a new parameter selection criterion based on uniformity and independence of probability integral transforms, enhancing density forecast validation during crises.

Findings

COVID-19 had a limited impact on Chinese markets

US markets experienced a strong impact

European markets showed slow recovery

Abstract

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.