Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student’s t-distribution

Risk management and prediction of market losses of cryptocurrencies are of notable value to risk managers, portfolio managers, financial market researchers and academics. One of the most common measures of an asset’s risk is Value-at-Risk (VaR). This paper evaluates and compares the performance of generalized autoregressive score (GAS) combined with heavy-tailed distributions, in estimating the VaR of two well-known cryptocurrencies’ returns, namely Bitcoin returns and Ethereum returns. In this paper, we proposed a VaR model for Bitcoin and Ethereum returns, namely the GAS model combined with the generalized lambda distribution (GLD), referred to as the GAS-GLD model. The relative performance of the GAS-GLD models was compared to the models proposed by Troster et al. (2018), in other words, GAS models combined with asymmetric Laplace distribution (ALD), the asymmetric Student’s t-distribution (AST) and the skew Student’s t-distribution (SSTD). The Kupiec likelihood ratio test was used to assess the adequacy of the proposed models. The principal findings suggest that the GAS models with heavy-tailed innovation distributions are, in fact, appropriate for modelling cryptocurrency returns, with the GAS-GLD being the most adequate for the Bitcoin returns at various VaR levels, and both GAS-SSTD, GAS-ALD and GAS-GLD models being the most appropriate for the Ethereum returns at the VaR levels used in this study.

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An empirical application of a stochastic volatility model with GH skew Student's t -distribution to the volatility of Latin-American stock returns

The Quarterly Review of Economics and Finance ◽

10.1016/j.qref.2018.01.002 ◽

2018 ◽

Vol 69 ◽

pp. 155-173 ◽

Cited By ~ 2

Author(s):

Patricia Lengua Lafosse ◽

Gabriel Rodríguez

Keyword(s):

Stock Returns ◽

Stochastic Volatility ◽

Latin American ◽

Stochastic Volatility Model ◽

Empirical Application ◽

Student’S T Distribution ◽

Volatility Model ◽

Student’S T ◽

Student's T Distribution ◽

T Distribution

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Robust Interacting Multiple Model Filter Based on Student’s t-Distribution for Heavy-Tailed Measurement Noises

Sensors ◽

10.3390/s19224830 ◽

2019 ◽

Vol 19 (22) ◽

pp. 4830

Author(s):

Dong Li ◽

Jie Sun

Keyword(s):

Interacting Multiple Model ◽

Multiple Model ◽

Student’S T Distribution ◽

Target State ◽

Measurement Noises ◽

Heavy Tailed ◽

Student’S T ◽

Scale Matrix ◽

Student's T Distribution ◽

T Distribution

In maneuvering target tracking applications, the performance of the traditional interacting multiple model (IMM) filter deteriorates seriously under heavy-tailed measurement noises which are induced by outliers. A robust IMM filter utilizing Student’s t-distribution is proposed to handle the heavy-tailed measurement noises in this paper. The measurement noises are treated as Student’s t-distribution, whose degrees of freedom (dof) and scale matrix are assumed to be governed by gamma and inverse Wishart distributions, respectively. The mixing distributions of the target state, dof, and scale matrix are achieved through the interacting strategy of IMM filter. These mixing distributions are used for the initialization of time prediction. The posterior distributions of the target state, dof, and scale matrix conditioned on each mode are obtained by employing variational Bayesian approach. Then, the target state, dof, and scale matrix parameters are jointly estimated. A variational method is also given to estimate the mode probability. The unscented transform is utilized to solve the nonlinear estimation problem. Simulation results show that the proposed filter improves the estimation accuracy of target state and mode probability over existing filters under heavy-tailed measurement noises.

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Radio Interferometric Calibration Using a Complex Student’s t-distribution and Wirtinger Derivatives

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz3037 ◽

2019 ◽

Cited By ~ 1

Author(s):

U M Sob ◽

H L Bester ◽

O M Smirnov ◽

J S Kenyon ◽

T L Grobler

Keyword(s):

Radio Frequency ◽

Dynamic Range ◽

Likelihood Function ◽

Real Data ◽

Radio Frequency Interference ◽

Student’S T Distribution ◽

Heavy Tailed ◽

Student’S T ◽

Student's T Distribution ◽

T Distribution

Abstract Radio interferometric gain calibration can be biased by incomplete sky models and radio frequency interference, resulting in calibration artefacts that can restrict the dynamic range of the resulting images. It has been suggested that calibration algorithms employing heavy-tailed likelihood functions are less susceptible to this due to their robustness against outliers in the data. We present an algorithm based on a Student’s t-distribution which leverages the framework of complex optimisation and Wirtinger calculus for efficient and robust interferometric gain calibration. We integrate this algorithm as an option in the newly released calibration software package, CubiCal. We demonstrate that the algorithm can mitigate some of the biases introduced by incomplete sky models and radio frequency interference by applying it to both simulated and real data. Our results show significant improvements compared to a conventional least-squares solver which assumes a Gaussian likelihood function. Furthermore, we provide some insight into why the algorithm outperforms the conventional solver, and discuss specific scenarios (for both direction-independent and direction-dependent self-calibration) where this is expected to be the case.

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