A Study Of Copula-Based Decision Tree With Applications

The application of Copula is lengthening day-by-day in many fields of sciences.It has been considered widely in the literature for the last several years.The reason for its attractiveness is twofold.First,it helps in studying scale-free measures of association.Second,it provides bases for the construction of multivariate distribution.In applied statistics and finance,the Copula has been exposed to be an established instrument for displaying complex dependencies.Copula extracts multivariate marginals from dependence structures so that the specification of dependence structure can be considered separately from marginal distributions.It can offer a flexible appliance for demonstrating real-life scattering that cannot be handled well by graphical models.Therefore,investigators have tried to link Copulas with graphical models,such as Canonical vine,Bayesian copula networks and tree-structure copula models.This dissertation contains four essays;all these essays' central idea is to focus on copula application.In the first essay,we establish an efficient decision tree data mining technique for two random variables based on Copula using mutual information coefficient as a classification index.The second essay is the application of two variable choice trees.The third essay explores Pakistan's foreign currency market with the conditional copula model's help through an engineered mechanism.The fourth essay investigates the dependence structure of microeconomic variables on oil prices through the Copula autoregressive model of order one.In particular,we propose a novel dynamic method that combines Copula's application with a novel co-efficient dependence(MIC)to construct a variable decision tree.Furthermore,with the help of the common factor copula model,we propose an innovative technique of evaluating government performance in the foreign currency market in a country.The organization of this Ph D dissertation is structured as follows.Chapter-1 introduces the copula concept in detail,throws light on the copula's advantages and limitations in a wider context,presents a brief literature review,a gap analysis,and main contribution to the literature.Chapter-2 introduces an innovative copula-based decision tree for random variables,consuming mutual information coefficient as splitting criteria to overcome the accuracy associated with decision trees.To classify the data while retaining its merit,a decision tree through Copula is proposed to classify the data efficiently and rank the important factors.The proposed method is then applied to two real-life data sets of credit card data for Taiwan and Pakistan's coronary heart disease data for illustration purposes.As an outcome,the proposed technique of introducing copula-based decision trees was established as useful tool for classification,prediction,and ranking of important factors in finance,statistics,machine learning,and several other related fields of decision sciences.Chapter-3 is applying the decision tree proposed in chapter two to identify and predict important factors that significantly influence secondary school student performance in Portugal.This research aims to improve Portugal's secondary school student performance by employing a decision tree,which is a useful data mining technique used for classification,prediction,and exploring factors by their importance.Results show that provided the first and/or second school periods,grades are available,and good predictive accuracy can be accomplished.Although student achievement is highly influenced by father job;an explanatory analysis has shown that there are also other factors(e.g.,study time,mother job,desire of higher education,paid class and travel time from school to home etc.)which are the key factors having a significant influence on student achievements at secondary level education in Portugal.As a direct outcome of this research,by focusing on these factors and making policies based on such research at the national level,the quality of education can be improved at the secondary level,which affects the higher education level in Europe.Chapter-4 introduces a unique method of government performance evaluation from foreign currency returns through common factor copula model,which explores governments' performance in the country.We achieved the objective differently.We hired an inverse method of assessment,with the factor copula model application,to study the dependence relationship of exchange rate returns as auxiliary variables.The performance of political and army government tenures in the country in the last two decades is evaluated.Through factor analysis,common factors for the exchange rate are acquired.The analysis shows that conditioned on the common factors,the dependence between the selected currencies was strongly asymmetric in most of the tenures except Pakistan Muslim League-Nawaz's condition,and the condition on common factor Clayton copula model supposition is more appropriate.Although we perceive high left tail dependence among foreign currency returns during Pakistan,Muslim League-Nawaz tenure,and the condition of common factor Gumbel copula model hypothesis is more suitable.In this way,we signify the foulest government performance in the country among all occupancies under consideration.Chapter-5 introduces the novel copula autoregressive model's application to investigate the dependence structure among macrofinancial variables using current monthly data of the Pakistan economic system starting from 2008-01 to 2020–04.This investigation considers a unique copulaautoregressive model approach to model nonlinear dependence structure amongst multiple time series.Having gain from the flexibleness of R-vine copulas,the autoregressive copula model with efficiency investigates the impact of one-time series on some others: it is;one-time series normally plays a vital role.We investigate the oil price effects on industrial production,inflation rate,and interest rate in Pakistan through the model's quality.One of the key findings of this analysis is that there is a weak tail asymmetry,however some tail dependence,that COPAR-model with efficiency absorbs into account.Furthermore,the fashion monitor lagged interest rate reactions and industrial production to fuel price adjustments inside Pakistan.The oil price result on the inflation rate,on the other hand,is quite simultaneous.Finally,Chapter-6 concludes this thesis and outlines the scope for future work.In summary,this thesis proposed a method for classification,prediction,and dependence models,including copula-based decision tree,the common factor copula model,and the copula autoregressive model.These three methods,which do not enforce any restriction on the dependence structure,can be used for prediction and demonstrate diverse high-dimensional reliance,such as tail dependence /asymmetry.Altogether,these methods are verified on real-life data sets,such as banking and finance,heart diseases,secondary school student performance,foreign currency exchange rate,returns,and macrofinancial indicators.This thesis' s mechanism shows that there are countless prospective in relating copula to model composite dependency,specifically in demonstrating a stochastic process or in developing capable vine copula generalization approaches.