The risk function of the goodness-of-fit tests for tail models

Hoffmann, Ingo; Börner, Christoph J.

doi:10.1007/s00362-020-01159-3

“…The approach taken here is to apply a modified version of the Anderson-Darling right-tail-weighted distance (RTAD) measure (see Chernobai et al [2005] and Hoffmann and Börner [2020]) to select a candidate pair of parameters, and then apply of an adaptation of the Cramer von Mises (CVM) test (see Choulakian and Stephens [2001]) to assess the plausibility that the observed data may be described by a GPD with these parameter estimates.…”

Section: Selecting a Set Of Parameter Estimatesmentioning

confidence: 99%

Chasing the Tail: A Generalized Pareto Distribution Approach to Estimating Wealth Inequality

Kennickell

¹

2023

Preprint

1

0

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Since the work reported in Vermeulen [2018], a literature has developed on using the simple Pareto distribution along with “rich list” information to make improved estimates of the upper tail of the wealth distribution measured in surveys. Because the construction of such external data is typically opaque and subject to potentially serious measurement error, it may be best not to depend exclusively on this approach. This paper develops an alternative approach, using the generalized Pareto distribution (GPD), of which the simple Pareto is a subset, extending an estimation strategy developed by Castillo and Hadi [1997]. The greater flexibility of the GPD allows the possibility of modeling the tail of the wealth distribution, using a larger set of data for support than is typically the case with the simple Pareto. Moreover, the elaboration of the estimation method presented here allows explicitly for the possibility that the extreme of the observed upper tail is measured with error or that it is not captured at all. The approach also allows the incorporation of external data on total wealth as a constraint on the estimation. For the applications considered here using Austrian and U.S. micro data, the model relies on an estimate of total household wealth from national accounts, rather than rich-list information. The results suggest that where sufficiently comparable and reliable estimates of aggregate wealth are available, this approach can provide a useful way of mitigating problems in comparing distributional estimates across surveys that differ meaningfully in their effective coverage of the upper tail of the wealth distribution. The approach may be particularly useful in the construction of distributional national accounts.

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“…The approach taken here is to apply a modified version of the Anderson-Darling right-tail-weighted distance (RTAD) measure (see Chernobai et al [2005] and Hoffmann and Börner [2020]) to select a candidate pair of parameters, and then apply of an adaptation of the Cramer von Mises (CVM) test (see Choulakian and Stephens [2001]) to assess the plausibility that the observed data may be described by a…”

Section: Selecting a Set Of Parameter Estimatesmentioning

confidence: 99%

Chasing the Tail: A Generalized Pareto Distribution Approach to Estimating Wealth Inequality

Kennickell¹

2021

Preprint

3

0

View full text Add to dashboard Cite

Since the work reported in Vermeulen [2018], a literature has developed on using the simple Pareto distribution along with “rich list” information to make improved estimates of the upper tail of the wealth distribution measured in surveys. Because the construction of such external data is typically opaque and subject to potentially serious measurement error, it may be best not to depend exclusively on this approach. This paper develops an alternative approach, using the generalized Pareto distribution (GPD), of which the simple Pareto is a subset, extending an estimation strategy developed by Castillo and Hadi [1997]. The greater flexibility of the GPD allows the possibility of modeling the tail of the wealth distribution, using a larger set of data for support than is typically the case with the simple Pareto. Moreover, the elaboration of the estimation method presented here allows explicitly for the possibility that the extreme of the observed upper tail is measured with error or that it is not captured at all. The approach also allows the incorporation of external data on total wealth as a constraint on the estimation. For the applications considered here using Austrian and U.S. micro data, the model relies on an estimate of total household wealth from national accounts, rather than rich-list information. The results suggest that where sufficiently comparable and reliable estimates of aggregate wealth are available, this approach can provide a useful way of mitigating problems in comparing distributional estimates across surveys that differ meaningfully in their effective coverage of the upper tail of the wealth distribution. The approach may be particularly useful in the construction of distributional national accounts. (Stone Center on Socio-Economic Inequality Working Paper)

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Assessing the Risk Characteristics of the Cryptocurrency Market: A GARCH-EVT-Copula Approach

Bruhn

¹

,

Ernst

²

2022

JRFM

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The cryptocurrency market offers significant investment opportunities but also entails higher risks as compared to other asset classes. This article aims to analyse the financial risk characteristics of individual cryptocurrencies and of a broad cryptocurrency market portfolio. We construct a portfolio comprising the 20 largest cryptocurrencies, which cover 82.1% of the total cryptocurrency market. The returns are examined for extreme tail risks by the application of Extreme Value Theory. We utilise the GARCH-EVT approach in combination with a novel algorithm to automatically determine the optimal threshold to model the tail distribution. Furthermore, we aggregate the individual market risks with a t-Student Copula to investigate possible diversification effects on a portfolio level. The empirical analysis indicates that all examined cryptocurrencies show high volatility in their price movements, whereby Bitcoin acts as the most stable cryptocurrency. All return distributions are heavy-tailed and subject to extreme tail risks. We find strong, positive intra-market correlations, in particular with the two largest cryptocurrencies Bitcoin and Ethereum. No diversification effect can be achieved by aggregating market risks. On the contrary, a negligibly lower expected return and higher joint extreme returns can be observed. From this analysis, it can be concluded that investments in individual cryptocurrencies as well as in a portfolio show extreme risks of losses. From the investor’s point of view, a possible strategy of risk reduction through portfolio formation within cryptocurrencies is only promising to a limited extent and does not offer a satisfactory solution to significantly reduce the risk within this asset class.

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The risk function of the goodness-of-fit tests for tail models

Cited by 4 publications

References 19 publications

Chasing the Tail: A Generalized Pareto Distribution Approach to Estimating Wealth Inequality

Chasing the Tail: A Generalized Pareto Distribution Approach to Estimating Wealth Inequality

Chasing the Tail: A Generalized Pareto Distribution Approach to Estimating Wealth Inequality

Assessing the Risk Characteristics of the Cryptocurrency Market: A GARCH-EVT-Copula Approach

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