English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A large consensus now seems to take for granted that the distributions ofempirical returns of financial time series are regularly varying, with a tailexponent close to 3. We revisit this results and use standard tests as well asdevelop a battery of new non-parametric and parametric tests (in particularwith stretched exponential (SE) distributions) to characterize thedistributions of empirical returns of financial time series, with applicationto the 100 years of daily return of the Dow Jones Industrial Average and over 1years of 5-minutes returns of the Nasdaq Composite index. Based on thediscovery that the SE distribution tends to the Pareto distribution in acertain limit such that the Pareto (or power law) distribution can beapproximated with any desired accuracy on an arbitrary interval by a suitableadjustment of the parameters of the SE distribution, we demonstrate that Wilks'test of nested hypothesis still works for the non-exactly nested comparisonbetween the SE and Pareto distributions. The SE distribution is foundsignificantly better over the whole quantile range but becomes unnecessarybeyond the 95% quantiles compared with the Pareto law. Similar conclusions holdfor the log-Weibull model with respect to the Pareto distribution. Our mainresult is that the tails ultimately decay slower than any stretched exponentialdistribution but probably faster than power laws with reasonable exponents.Implications of our results on the ``moment condition failure'' and for riskestimation and management are presented.

Empirical Distributions of Log-Returns: Between the Stretched Exponential and the Power Law?