Browsing by Subject "Extreme value theory"

Now showing 1 - 5 of 5

Open Access
Analysis of DF relay selection in massive MIMO systems with hardware ımpairments
(IEEE, 2020) Kazemi, M.; Mohammadi, A.; Duman, Tolga M.
We consider a massive multiple-input multiple-output (m-MIMO) system in which a source communicates with a destination with the help of multiple single-antenna decode-and-forward (DF) relays. Employing optimal relay selection, we analyze the system performance in presence of hardware impairments (HWI) for two m-MIMO scenarios: massive-antenna source and single-antenna destination (m-MIMO I), and massive-antenna source and destination (m-MIMO II). We obtain lower bounds on the average signal-to-noise plus distortion ratio (SNDR) of the system and show that in the m-MIMO II regime, the HWI levels at the relays become the only limiting factors. Employing extreme value theory, we demonstrate that as the number of relays increases the end-to-end SNDR of the system tends to Gumbel and Weibull distributions for the m-MIMO I and m-MIMO II systems, respectively. In addition, for both arbitrary numbers of source and destination antennas and m-MIMO scenarios, we provide closed form expressions for optimal power allocation between the source and the selected relay, and the effects of HWI level distributions between the receiving and the transmitting parts of the relay (which can be exploited for optimal system design under cost constraints).
Open Access
EVIM: a software package for extreme value analysis in MATLAB
(Walter de Gruyter GmbH, 2001) Gençay, R.; Selçuk, F.; Ulugülyagci, A.
From the practitioners' point of view, one of the most interesting questions that tail studies can answer is what are the extreme movements that can be expected in financial markets? Have we already seen the largest ones or are we going to experience even larger movements? Are there theoretical processes that can model the type of fat tails that come out of our empirical analysis? Answers to such questions are essential for sound risk management of financial exposures. It turns out that we can answer these questions within the framework of the extreme value theory. This paper provides a step-by-step guideline for extreme value analysis in the MATLAB environment with several examples.
Open Access
Extreme value theory and Value-at-Risk: relative performance in emerging markets
(Elsevier BV, 2004) Gençay, R.; Selçuk, F.
In this paper, we investigate the relative performance of Value-at-Risk (VaR) models with the daily stock market returns of nine different emerging markets. In addition to well-known modeling approaches, such as variance-covariance method and historical simulation, we study the extreme value theory (EVT) to generate VaR estimates and provide the tail forecasts of daily returns at the 0.999 percentile along with 95% confidence intervals for stress testing purposes. The results indicate that EVT-based VaR estimates are more accurate at higher quantiles. According to estimated Generalized Pareto Distribution parameters, certain moments of the return distributions do not exist in some countries. In addition, the daily return distributions have different moment properties at their right and left tails. Therefore, risk and reward are not equally likely in these economies. (C) 2004 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
Open Access
High volatility, thick tails and extreme value theory in value-at-risk estimation
(Elsevier BV, 2003) Gençay, R.; Selçuk, F.; Ulugülyaǧci, A.
In this paper, the performance of the extreme value theory in value-at-risk calculations is compared to the performances of other well-known modeling techniques, such as GARCH, variance-covariance (Var-Cov) method and historical simulation in a volatile stock market. The models studied can be classified into two groups. The first group consists of GARCH(1, 1) and GARCH(1, 1)- t models which yield highly volatile quantile forecasts. The other group, consisting of historical simulation, Var-Cov approach, adaptive generalized Pareto distribution (GPD) and nonadaptive GPD models, leads to more stable quantile forecasts. The quantile forecasts of GARCH(1, 1) models are excessively volatile relative to the GPD quantile forecasts. This makes the GPD model be a robust quantile forecasting tool which is practical to implement and regulate for VaR measurements. © 2003 Elsevier B.V. All rights reserved.
Open Access
Overnight borrowing, interest rates and extreme value theory
(Elsevier BV, 2006) Gençay, R.; Selçuk, F.
We examine the dynamics of extreme values of overnight borrowing rates in an inter-bank money market before a financial crisis during which overnight borrowing rates rocketed up to (simple annual) 4000 percent. It is shown that the generalized Pareto distribution fits well to the extreme values of the interest rate distribution. We also provide predictions of extreme overnight borrowing rates using pre-crisis data. The examination of tails (extreme values) provides answers to such issues as to what are the extreme movements to be expected in financial markets; is there a possibility for even larger movements and, are there theoretical processes that can model the type of fat-tails in the observed data? The answers to such questions are essential for proper management of financial exposures and laying ground for regulations. © 2005 Elsevier B.V. All rights reserved.