Volatility filtering in estimation of kurtosis (and variance)

The kurtosis of the distribution of financial returns characterized by high volatility persistence and thick tails is notoriously difficult to estimate precisely. We propose a simple but effective procedure of estimating the kurtosis coefficient (and variance) based on volatility filtering that uses a simple GARCH model. In addition to an estimate, the proposed algorithm issues a signal of whether the kurtosis (or variance) is finite or infinite. We also show how to construct confidence intervals around the proposed estimates. Simulations indicate that the proposed estimates are much less median biased than the usual method-of-moments estimates, their confidence intervals having much more precise coverage probabilities. The procedure alsoworks well when the underlying volatility process is not the one the filtering technique is based on. We illustrate how the algorithm works using several actual series of returns.

Skewed Wealth Distributions: Theory and Empirics

Invariably, across a cross-section of countries and time periods, wealth distributions are skewed to the right displaying thick upper tails, that is, large and slowly declining top wealth shares. In this survey, we categorize the theoretical studies on the distribution of wealth in terms of the underlying economic mechanisms generating skewness and thick tails. Further, we show how these mechanisms can be micro-founded by the consumption–savings decisions of rational agents in specific economic and demographic environments. Finally we map the large empirical work on the wealth distribution to its theoretical underpinnings. (JEL C46, D14, D31, E21, J31)

An opportunity of application of excess factor in hydrology

In last few years in hydrology an interest to excess factor has appeared as a reaction to unsuccessful attempts to simulate and predict evolving hydrological processes, which attributive property is statistical instability. The article shows, that the latter has a place at strong relative multiplicative noises of probabilistic stochastic model of a river flow formation, phenomenological display of which are "the thick tails" and polymodality, for which the excess factor "answers", by being ignored by a modern hydrology in connection to the large error of its calculation because of insufficient duration of lines of observation over a flow. However, it is found out, that the duration of observation of several decades practically stabilizes variability of the excess factor, the error of which definition appears commensurable with an error of other calculated characteristics used in engineering hydrology.