Recent constructions of low-discrepancy sequences

Niederreiter, Harald

doi:10.1016/j.matcom.2014.10.001

Cited by 2 publications

(1 citation statement)

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“…We thus use an additional criterion coming from the literature of simulation of quasi-random variables. We indeed want our series of PITs to be a low-discrepancy sequence [27,39,28]. This is even more important that we want to estimate a time-varying density of price returns in a regime-switching market.…”

Section: Selection Of the Bandwidth And Of The Discount Factormentioning

confidence: 99%

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

Garcin¹,

Klein²,

Laaribi³

2020

Preprint

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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.

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Section: Selection Of the Bandwidth And Of The Discount Factormentioning

confidence: 99%