A VaR assuming Student t distribution not significantly different from a VaR assuming normal distribution

2017 ◽  
Vol 19 (3) ◽  
pp. 189-201
Author(s):  
Su Xu
Keyword(s):  
Normal Distribution ◽  
Student T Distribution ◽  
T Distribution

scholarly journals The Beta-Hyperbolic Secant Distribution

2016 ◽  
Vol 39 (3) ◽  
Author(s):  
Matthias J. Fischer ◽  
David Vaughan
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Glass Fibre ◽  
Goodness Of Fit ◽  
Weighting Function ◽  
Logistic Distribution ◽  
Student T Distribution ◽  
T Distribution ◽  
Skewness And Kurtosis

The shape of a probability distribution is often summarized by the distribution’s skewness and kurtosis. Starting from a symmetric “parent” density f on the real line, we can modify its shape (i.e. introduce skewness and in-/decrease kurtosis) if f is appropriately weighted. In particular, every density w on the interval (0; 1) is a specific weighting function. Within this work, we follow up a proposal of Jones (2004) and choose the Beta distribution asunderlying weighting function w. “Parent” distributions like the Student-t, the logistic and the normal distribution have already been investigated in the literature. Based on the assumption that f is the density of a hyperbolic secant distribution, we introduce the Beta-hyperbolic secant (BHS) distribution. In contrast to the Beta-normal distribution and to the Beta-Student-t distribution, BHS densities are always unimodal and all moments exist. In contrast to the Beta-logistic distribution, the BHS distribution is more flexibleregarding the range of skewness and leptokurtosis combinations. Moreover,we propose a generalization which nests both the Beta-logistic and the BHS distribution. Finally, the goodness-of-fit between all above-mentioned distributions is compared for glass fibre data and aluminium returns.

scholarly journals Modeling and forecasting volatility in global food commodity prices

2011 ◽  
Vol 57 (No. 3) ◽  
pp. 132-139 ◽  
Author(s):  
I.A. Onour ◽  
B.S. Sergi
Keyword(s):  
Normal Distribution ◽  
Commodity Prices ◽  
Distribution Model ◽  
Distribution Models ◽  
Student T Distribution ◽  
Competing Models ◽  
Forecasting Volatility ◽  
T Distribution ◽  
Food Commodity ◽  
Global Food

To capture the volatility in the global food commodity prices, we employed two competing models, the thin tailed the normal distribution, and the fat-tailed Student t-distribution models. Results based on wheat, rice, sugar, beef, coffee, and groundnut prices, during the sample period from October 1984 to September 2009, show the t-distribution model outperforms the normal distribution model, suggesting that the normality assumption of residuals which are often taken for granted for its simplicity may lead to unreliable results of the conditional volatility estimates. The paper also shows that the volatility of food commodity prices characterized with the intermediate and short memory behavior, implying that the volatility of food commodity prices is mean reverting.

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

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3611
Author(s):  
Yang Gong ◽  
Chen Cui
Keyword(s):  
Target Tracking ◽  
Sequential Monte Carlo ◽  
Measurement Noise ◽  
Particle Simulation ◽  
Target Number ◽  
Student T Distribution ◽  
Multi Target Tracking ◽  
Heavy Tailed ◽  
Scale Matrix ◽  
T Distribution

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.

scholarly journals Power Birnbaum-Saunders Student t distribution

2017 ◽  
Vol 35 (1) ◽  
pp. 51-70
Author(s):  
Germán Moreno-Arenas ◽  
◽  
Guillermo Martínez-Flórez ◽  
Heleno Bolfarine ◽  
◽  
...  
Keyword(s):  
Student T Distribution ◽  
T Distribution

JUMP, NON-NORMAL ERROR DISTRIBUTION AND STOCK PRICE VOLATILITY — A NONPARAMETRIC SPECIFICATION TEST

2009 ◽  
Vol 54 (01) ◽  
pp. 101-121
Author(s):  
MOHAMMAD MASUDUR RAHMAN ◽  
LAILA ARJUMAN ARA ◽  
ZHENLONG ZHENG
Keyword(s):  
Stock Price ◽  
Stock Return ◽  
Garch Model ◽  
Price Volatility ◽  
Stock Index ◽  
Specification Test ◽  
Significance Level ◽  
Student T Distribution ◽  
T Distribution ◽  
Distribution Assumption

This paper examines a wide variety of popular volatility models for stock index return, including Random Walk model, Autoregressive model, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, and extensive GARCH model, GARCH-jump model with Normal, and Student t-distribution assumption as well as nonparametric specification test of these models. We fit these models to Dhaka stock return index from 20 November 1999 to 9 October 2004. There has been empirical evidence of volatility clustering, alike to findings in previous studies. Each market contains different GARCH models, which fit well. From the estimation, we find that the volatility of the return and the jump probability were significantly higher after 27 November 2001. The model introducing GARCH jump effect with normal and Student t-distribution assumption can better fit the volatility characteristics. We find that RW-GARCH-t, RW-AGARCH-t RW-IGARCH-t and RW-GARCH-M-t can pass the nonparametric specification test at 5% significance level. It is suggested that these four models can capture the main characteristics of Dhaka stock return index.

Performance of Empirical Bayes Estimators of Level-2 Random Parameters in Multilevel Analysis: A Monte Carlo Study for Longitudinal Designs

2003 ◽  
Vol 28 (2) ◽  
pp. 169-194 ◽  
Author(s):  
Math J. J. M. Candel ◽  
Bjorn Winkens
Keyword(s):  
Monte Carlo ◽  
Normal Distribution ◽  
Multilevel Analysis ◽  
Empirical Bayes ◽  
Ordinary Least Squares ◽  
Random Coefficients ◽  
Bayes Estimator ◽  
Performance Criteria ◽  
Random Parameters ◽  
T Distribution

Multilevel analysis is a useful technique for analyzing longitudinal data. To describe a person’s development across time, the quality of the estimates of the random coefficients, which relate time to individual changes in a relevant dependent variable, is of importance. The present study compares three estimators of the random coefficients: the Bayes estimator (BE), the empirical Bayes estimator (EBE), and the ordinary least squares estimator (OLSE). Using MLwiN, Monte Carlo simulations are carried out to study the performance of the estimators, while systematically varying the size of the sample as well as the number of measurement occasions. First, we examine for normally distributed random coefficients to what extent the EBE performs better than the OLSE and to what extent the EBE preserves the good properties of the BE. Second, we examine the robustness of the EBE which is based on a normal distribution of the random parameters, by comparing its performance to the OLSE for data being generated from two distributions other than the normal distribution: a modified t-distribution and a modified exponential distribution. As performance criteria we examine the Bayes risk as well as a criterion based on the frequentist notion of mean squared error.

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