scholarly journals Risk, VaR, CVaR and Their Associated Portfolio Optimizations When Asset Returns Have a Multivariate Student T Distribution

2011 ◽  
Author(s):  
William Thornton Shaw
Keyword(s):  
Asset Returns ◽  
Student T Distribution ◽  
T Distribution

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.

Multivariate measurement error models based on Student-t distribution under censored responses

Statistics ◽  
2018 ◽  
Vol 52 (6) ◽  
pp. 1395-1416 ◽  
Author(s):  
Larissa A. Matos ◽  
Luis M. Castro ◽  
Celso R. B. Cabral ◽  
Víctor H. Lachos
Keyword(s):  
Measurement Error ◽  
Error Models ◽  
Measurement Error Models ◽  
Student T Distribution ◽  
T Distribution
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