Journal of Data Science

Abstract: Crude oil being the primary source of energy is been unquestioningly the main driving engine of every country in this world whether it is the oil producer economy and/or oil consumer economy. Crude oil, one of the key strategic products in the global market, may influence the economy of the exporting and importing countries. Iran is one of the major crude oil exporting partners of the Organization of the Petroleum Exporting Countries (OPEC). Analysis of the risk measures associated with the Iranian oil price data is of strategic importance to the Iranian government and policy makers in particular for the short-and long-term planning for setting up the oil production targets. Oil price risk-management focuses mainly on when and how an organization can best prevent the costly exposure to the price risk. Value-at-Risk (VaR) is the commonly accepted instrument of risk-measure and is evaluated by analysing the negative tail of the probability distributions of the returns/profit and loss. Among several approaches for calculating VaR, the most common approaches are variance-covariance approach, historical simulation and Monte-Carlo simulation. Recently, copula functions have emerged as a powerful tool to model and simulate multivariate probability distributions. Copula applications have been noted predominantly in the areas of finance, actuary, economics and health and clinical studies. In addition, copulas are useful devices to deal with the non normality and non-linearity issues which are frequently observed in cases of financial time series data. In this paper we shall apply copulas namely; Frank copula, Clayton copula and Gumbel copula to analyse the time series crude oil price data of Iran in respect of OPEC prices. Data considered are; i. Monthly average prices for a barrel of Iranian and OPEC crude oil, from January 1997 to December 2008, ii. Seasonal number of barrels of Iran’s crude oil export, from January 1997 to December 2008. The results will demonstrate copula simulated data are providing higher and lower relative change values on the upper and lower tails respectively in comparison to the original data.

Abstract: In modeling and analyzing multivariate data, the conventionally used measure of dependence structure is the Pearson’s correlation coeffi cient. However use of the correlation as a dependence measure has several pitfalls. Copulas recently have emerged as an alternative measure of the de pendence, overcoming most of the drawbacks of the correlation. We discuss Archimedean copulas and their relationships with tail dependence. An algo rithm to construct empirical and Archimedean copulas is described. Monte Carlo simulations are carried out to replicate and analyze data sets by iden tifying the appropriate copula. We apply the Archimedean copula based methodology to assess the accuracy of Doppler echocardiography in deter mining aortic valve area from the Aortic Stenosis: Simultaneous Doppler – Catheter Correlative study carried out at the King Faisal Specialist Hospital and Research Centre, Riyadh, KSA