Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability

Paolella, Marc S.

doi:10.3390/econometrics4020025

Cited by 19 publications

(9 citation statements)

References 99 publications

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“…A contingency-based strategy proposes maximization of true positive (TP) values and minimization of false negative (FN) and false positive (FP) values [43]. Finally, another distribution testing procedure has been proposed in [44].…”

Section: Further Discussionmentioning

confidence: 99%

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

Jäntschi

2019

Symmetry

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One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling distribution) provides rich information for any estimation to be made. Distributions are split into two main groups: continuous and discrete. The present study applies to continuous distributions. One of the challenges of sampling is its accuracy, or, in other words, how representative the sample is of the population from which it was drawn. To answer this question, a series of statistics have been developed to measure the agreement between the theoretical (the population) and observed (the sample) distributions. Another challenge, connected to this, is the presence of outliers - regarded here as observations wrongly collected, that is, not belonging to the population subjected to study. To detect outliers, a series of tests have been proposed, but mainly for normal (Gauss) distributions—the most frequently encountered distribution. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect outliers by constructing the confidence interval for the extreme value in the sample, at a certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (with a known probability density function) and is also dependent on the statistical parameters of the population—here it is discussed in connection with estimating those parameters by the maximum likelihood estimation method operating on a uniform U(0,1) continuous symmetrical distribution.

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Section: Further Discussionmentioning

confidence: 99%

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

Jäntschi

2019

Symmetry

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“…It is noteworthy to mention that despite an adapted version of the SMOTE regression is used, most methodologies presented in this paper would not be suitable if the underlying returns were not i.i.d., and therefore, the resulting risk measures likely to be inadequate. Alternatives relying on time series processes, GARCH models for instance, might be of interest in such a situation (see [15,38,39] among others). For the methodologies requiring parameters to drive their behaviour, those obtained through the methodologies aforementioned are provided in Table 1.…”

Section: Risk Measurement-applicationmentioning

confidence: 99%

Expected Shortfall Reliability—Added Value of Traditional Statistics and Advanced Artificial Intelligence for Market Risk Measurement Purposes

Menéndez¹,

Hassani²

2021

Mathematics

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The Fundamental Review of the Trading Book is a market risk measurement and management regulation recently issued by the Basel Committee. This reform, often referred to as “Basel IV”, intends to strengthen the financial system. The newest capital standard relies on the use of the Expected Shortfall. This risk measure requires to get sufficient information in the tails to ensure its reliability, as this one has to be alimented by a sufficient quantity of relevant data (above the 97.5 percentile in the case of the regulation or interest). In this paper, after discussing the relevant features of Expected Shortfall for risk measurement purposes, we present and compare several methods allowing to ensure the reliability of the risk measure by generating information in the tails. We discuss these approaches with respect to their relevance considering the underlying situation when it comes to available data, allowing practitioners to select the most appropriate approach. We apply traditional statistical methodologies, for instance distribution fitting, kernel density estimation, Gaussian mixtures and conditional fitting by Expectation-Maximisation as well as AI related strategies, for instance a Synthetic Minority Over-sampling Technique implemented in a regression environment and Generative Adversarial Nets.

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“…To operationalize this, it is best to fit a GARCH model with stable Paretian innovations, termed an S α,β -GARCH process (as opposed to use of a two-step procedure based on quasi-ML), and then test if the filtered (location and time-varyingscale-standardized) returns follow a stable distribution. This is pursued in Paolella (2016), in which very fast, non-likelihood-based methods of estimation are proposed, this being relevant particularly when testing large numbers of series is of interest, and then the tests in this paper-with their fast calculation of p-values-can be applied. Observe that the validity of such an application depends on the extent to which the filtered innovation sequence (i) is close enough to being i.i.d., noting that any imposed GARCH-type process is surely wrong w.p.1, and (ii) its resulting distribution is "close" to that of the actual innovation sequence.…”

Section: Conclusion and Concurrent Researchmentioning

confidence: 99%

Asymmetric stable Paretian distribution testing

Paolella

2017

Econometrics and Statistics

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Two new tests for the symmetric stable Paretian distribution with tail index 1 α 2 are proposed. The test statistics and their associated approximate p-values are instantly computed and do not require use of the stable density or distribution or maximum likelihood estimation. They exhibit high power against a variety of alternatives, and much higher power than the existing test based on the empirical characteristic function. The two tests are combined to yield a test that has substantially higher power. A fourth test based on likelihood ratio is also studied. Extensions are proposed to address the asymmetric case and are shown to have reasonable actual size properties and high power against several viable alternatives.

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Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability

Cited by 19 publications

References 99 publications

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

Expected Shortfall Reliability—Added Value of Traditional Statistics and Advanced Artificial Intelligence for Market Risk Measurement Purposes

Asymmetric stable Paretian distribution testing

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