On the Lp-Norm Regression Models for Estimating Value-at-Risk

Kumar, Pranesh, and Kashanchi, Faramarz. "On the Lp-Norm Regression Models for Estimating Value-at-Risk." Serdica Journal of Computing 8.3 (2014): 255-268. <http://eudml.org/doc/270078>.

@article{Kumar2014,
abstract = {Analysis of risk measures associated with price series data movements and its predictions are of strategic importance in the financial markets as well as to policy makers in particular for short- and longterm planning for setting up economic growth targets. For example, oilprice risk-management focuses primarily on when and how an organization can best prevent the costly exposure to price risk. Value-at-Risk (VaR) is the commonly practised instrument to measure risk and is evaluated by analysing the negative/positive tail of the probability distributions of the returns (profit or loss). In modelling applications, least-squares estimation (LSE)-based linear regression models are often employed for modeling and analyzing correlated data. These linear models are optimal and perform relatively well under conditions such as errors following normal or approximately normal distributions, being free of large size outliers and satisfying the Gauss-Markov assumptions. However, often in practical situations, the LSE-based linear regression models fail to provide optimal results, for instance, in non-Gaussian situations especially when the errors follow distributions with fat tails and error terms possess a finite variance. This is the situation in case of risk analysis which involves analyzing tail distributions. Thus, applications of the LSE-based regression models may be questioned for appropriateness and may have limited applicability. We have carried out the risk analysis of Iranian crude oil price data based on the Lp-norm regression models and have noted that the LSE-based models do not always perform the best. We discuss results from the L1, L2 and L∞-norm based linear regression models. ACM Computing Classification System (1998): B.1.2, F.1.3, F.2.3, G.3, J.2.},
author = {Kumar, Pranesh, Kashanchi, Faramarz},
journal = {Serdica Journal of Computing},
keywords = {Value-at-Risk (VaR); Quantile Distributions; Least-Squares estimation; Lp-Norms},
language = {eng},
number = {3},
pages = {255-268},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On the Lp-Norm Regression Models for Estimating Value-at-Risk},
url = {http://eudml.org/doc/270078},
volume = {8},
year = {2014},
}

TY - JOUR
AU - Kumar, Pranesh
AU - Kashanchi, Faramarz
TI - On the Lp-Norm Regression Models for Estimating Value-at-Risk
JO - Serdica Journal of Computing
PY - 2014
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 8
IS - 3
SP - 255
EP - 268
AB - Analysis of risk measures associated with price series data movements and its predictions are of strategic importance in the financial markets as well as to policy makers in particular for short- and longterm planning for setting up economic growth targets. For example, oilprice risk-management focuses primarily on when and how an organization can best prevent the costly exposure to price risk. Value-at-Risk (VaR) is the commonly practised instrument to measure risk and is evaluated by analysing the negative/positive tail of the probability distributions of the returns (profit or loss). In modelling applications, least-squares estimation (LSE)-based linear regression models are often employed for modeling and analyzing correlated data. These linear models are optimal and perform relatively well under conditions such as errors following normal or approximately normal distributions, being free of large size outliers and satisfying the Gauss-Markov assumptions. However, often in practical situations, the LSE-based linear regression models fail to provide optimal results, for instance, in non-Gaussian situations especially when the errors follow distributions with fat tails and error terms possess a finite variance. This is the situation in case of risk analysis which involves analyzing tail distributions. Thus, applications of the LSE-based regression models may be questioned for appropriateness and may have limited applicability. We have carried out the risk analysis of Iranian crude oil price data based on the Lp-norm regression models and have noted that the LSE-based models do not always perform the best. We discuss results from the L1, L2 and L∞-norm based linear regression models. ACM Computing Classification System (1998): B.1.2, F.1.3, F.2.3, G.3, J.2.
LA - eng
KW - Value-at-Risk (VaR); Quantile Distributions; Least-Squares estimation; Lp-Norms
UR - http://eudml.org/doc/270078
ER -