MEASURING VALUE AT RISK USING GARCH MODEL - EVIDENCE FROM THE CRYPTOCURRENCY MARKET

There is a growing interest in the activities of the crypto market by various stakeholders. These stakeholders generally include investors, entrepreneurs, governments, fund managers, climate activists, institutional managers, employees with surplus funds, and crypto miners. This study aims to investigate the accuracy of the GARCH models for measuring and estimating Value-at-risk (VaR) using the Cryptocurrency index for future investment and managerial decision making. Because of this, the present study uses the top 30 Cryptocurrencies index in terms of Market capitalization excluding stable coins to determine the best GARCH models. Many entrepreneurs, institutional managers, fund managers, and other stakeholders have recently included cryptocurrency in their investment portfolio because of the increase in transactions and high returns growth in the global financial market with its associated high returns and volatility. Information communication technology has paved the way for such activities in the global markets. The daily data frequency was applied because of the availability of the data. The empirical analysis has been carried out for the period from January 2017 to December 2020 for a total of 1461observation. The returns volatility is estimated using SGARCH and EGARCH models. The findings evidenced that, using both normal distribution and Student t distribution, EGARCH provides a better measure and estimate than SGARCH concerning high persistence and volatility. Against this background, the present study also examined Backtesting to estimate Value at Risk. Interestingly, the findings of the available study would provide industry players, practitioners, entrepreneurs, and investors the maximum edge on how to use or measure such variables against others to make investment decisions. Also, the findings would subsequently contribute more insight into academia on the study area.

Improving Skin Cancer Classification Using Heavy-Tailed Student T-Distribution in Generative Adversarial Networks (TED-GAN)

Deep learning has gained immense attention from researchers in medicine, especially in medical imaging. The main bottleneck is the unavailability of sufficiently large medical datasets required for the good performance of deep learning models. This paper proposes a new framework consisting of one variational autoencoder (VAE), two generative adversarial networks, and one auxiliary classifier to artificially generate realistic-looking skin lesion images and improve classification performance. We first train the encoder-decoder network to obtain the latent noise vector with the image manifold’s information and let the generative adversarial network sample the input from this informative noise vector in order to generate the skin lesion images. The use of informative noise allows the GAN to avoid mode collapse and creates faster convergence. To improve the diversity in the generated images, we use another GAN with an auxiliary classifier, which samples the noise vector from a heavy-tailed student t-distribution instead of a random noise Gaussian distribution. The proposed framework was named TED-GAN, with T from the t-distribution and ED from the encoder-decoder network which is part of the solution. The proposed framework could be used in a broad range of areas in medical imaging. We used it here to generate skin lesion images and have obtained an improved classification performance on the skin lesion classification task, rising from 66% average accuracy to 92.5%. The results show that TED-GAN has a better impact on the classification task because of its diverse range of generated images due to the use of a heavy-tailed t-distribution.

Modeling the Exchange Rate Volatility Using the BRICS GARCH-type Models

The paper models the performance of GARCH-type models on BRICS exchange rates volatility. The levels of interdependence and dynamic connection among the BRICS financial markets using appropriate univariate time series models were evaluated for the period January 2008 to January 2018. The results revealed the presence of ARCH effects in the BRICS exchange rates. The univariate GARCH models for the BRICS exchange rates were fitted to the data using Student t-distribution. The GARCH (1,1) model found the unconditional volatility for each of the BRICS exchange rates series while EGARCH (1,1) and TGARCH (1,1) models presented the leverage effect. Moreover, the EGARCH (1,1) model illustrated that the asymmetric effects dominate the symmetric effects except for South Africa. The TGARCH (1,1) model on the other hand revealed contrary findings. The paper recommends a study be considered to draw comparison on the different types of GARCH models on the time varying integrated data other than the ones used in the paper.

The Type I Half Logistic Skew-t Distribution: A Heavy-Tail Model with Inverted Bathtub Shaped Hazard Rate

In this article a new generalization of the skew student-t distribution was introduced. The two-parameter model called the type I half-logistic skew-t (TIHLST) distribution can fit skewed, heavy-right tail, and long-tail datasets. Statistical properties of the type I half-logistic skew-t (TIHLST) distribution were derived and the maximum likelihood method parameter estimates assessed through a simulation study. A well-known dataset was analysed, illustrating the usefulness of the new distribution in modeling skewed and heavy-tailed data. The hazard rate shape was found to be increasing, decreasing and inverted bathtub shaped which was also reflected in the application result.

Correction to: Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution

A Correction to this paper has been published: 10.1007/s11075-021-01156-z

A Robust SMC-PHD Filter for Multi-Target Tracking with Unknown Heavy-Tailed Measurement Noise

In multi-target tracking, the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter is a practical algorithm. Influenced by outliers under unknown heavy-tailed measurement noise, the SMC-PHD filter suffers severe performance degradation. In this paper, a robust SMC-PHD (RSMC-PHD) filter is proposed. In the proposed filter, Student-t distribution is introduced to describe the unknown heavy-tailed measurement noise where the degrees of freedom (DOF) and the scale matrix of the Student-t distribution are respectively modeled as a Gamma distribution and an inverse Wishart distribution. Furthermore, the variational Bayesian (VB) technique is employed to infer the unknown DOF and scale matrix parameters while the recursion estimation framework of the RSMC-PHD filter is derived. In addition, considering that the introduced Student- t distribution might lead to an overestimation of the target number, a strategy is applied to modify the updated weight of each particle. Simulation results demonstrate that the proposed filter is effective with unknown heavy-tailed measurement noise.

Financial Time Series Analysis via Backtesting Approach

This book chapter investigated the place of backtesting approach in financial time series analysis in choosing a reliable Generalized Auto-Regressive Conditional Heteroscedastic (GARCH) Model to analyze stock returns in Nigeria. To achieve this, The chapter used a secondary data that was collected from www.cashcraft.com under stock trend and analysis. Daily stock price was collected on Zenith bank stock price from October 21st 2004 to May 8th 2017. The chapter used nine different GARCH models (standard GARCH (sGARCH), Glosten-Jagannathan-Runkle GARCH (gjrGARCH), Exponential GARCH (Egarch), Integrated GARCH (iGARCH), Asymmetric Power Autoregressive Conditional Heteroskedasticity (ARCH) (apARCH), Threshold GARCH (TGARCH), Non-linear GARCH (NGARCH), Nonlinear (Asymmetric) GARCH (NAGARCH) and The Absolute Value GARCH (AVGARCH) with maximum lag of 2. Most the information criteria for the sGARCH model were not available due to lack of convergence. The lowest information criteria were associated with apARCH (2,2) with Student t-distribution followed by NGARCH(2,1) with skewed student t-distribution. The backtesting result of the apARCH (2,2) was not available while eGARCH(1,1) with Skewed student t-distribution, NGARCH(1,1), NGARCH(2,1), and TGARCH (2,1) failed the backtesting but eGARCH (1,1) with student t-distribution passed the backtesting approach. Therefore with the backtesting approach, eGARCH(1,1) with student distribution emerged the superior model for modeling Zenith Bank stock returns in Nigeria. This chapter recommended the backtesting approach to selecting reliable GARCH model.