scholarly journals Fitting Compound Archimedean Copulas to Data for Modeling Electricity Demand

2021 ◽  
Vol 10 (5) ◽  
pp. 20
Author(s):  
Moshe Kelner ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Random Variables ◽  
Electricity Demand ◽  
Archimedean Copula ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Maximum Daily Temperature ◽  
Multiple Parameter ◽  
Original Family ◽  
Dependence Structures

Modeling dependence between random variables is accomplished effectively by using copula functions. Practitioners often rely on the single parameter Archimedean family which contains a large number of functions, exhibiting a variety of dependence structures. In this work we propose the use of the multiple-parameter compound Archimedean family, which extends the original family and allows more elaborate dependence structures. In particular, we use a copula of this type to model the dependence structure between the minimum daily electricity demand and the maximum daily temperature. It is shown that the compound Archimedean copula enhances the flexibility of the dependence structure and provides a better fit to the data.

scholarly journals Compound Archimedean Copulas

2021 ◽  
Vol 10 (3) ◽  
pp. 126
Author(s):  
Moshe Kelner ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Random Variables ◽  
Copula Function ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Unique Structure ◽  
The Family ◽  
The Many

The copula function is an effective and elegant tool useful for modeling dependence between random variables. Among the many families of this function, one of the most prominent family of copula is the Archimedean family, which has its unique structure and features. Most of the copula functions in this family have only a single dependence parameter which limits the scope of the dependence structure. In this paper we modify the generator of Archimedean copulas in a way which maintains membership in the family while increasing the number of dependence parameters and, consequently, creating new copulas having more flexible dependence structure.

Simulation for Mixture of Archimedean Copulas

2012 ◽  
Vol 195-196 ◽  
pp. 738-743
Author(s):  
Shi De Ou
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Tail Dependence ◽  
Likelihood Estimation ◽  
Numerical Results ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Models ◽  
Random Samples ◽  
Dependence Structures

Many dependence structures can consist of mixed copulas. In order to analyze the dependence of stock, we present the method of estimation for mixed copula models. Via generating random samples and using maximum likelihood estimation, the parameters of mixture of Archimedean copulas are estimated. Numerical results show that this method estimates effectively the parameters and tail dependence coefficients. Therefore we can use the method to analyze dependence structure for stocks.

On the optimal stopping values induced by general dependence structures

2001 ◽  
Vol 38 (3) ◽  
pp. 672-684 ◽  
Author(s):  
Alfred Müller ◽  
Ludger Rüschendorf
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Dependence Structure ◽  
Optimal Stopping Problem ◽  
Convex Order ◽  
Joint Distribution Function ◽  
Positive Dependence ◽  
Joint Distributions ◽  
Dependence Structures

The optimal stopping value of random variables X1,…,Xn depends on the joint distribution function of the random variables and hence on their marginals as well as on their dependence structure. The maximal and minimal values of the optimal stopping problem is determined within the class of all joint distributions with fixed marginals F1,…,Fn. They correspond to some sort of strong negative or positive dependence of the random variables. Any value inbetween these two extremes is attained for some dependence structures. The determination of the minimal value is based on some new ordering results for probability measures, in particular on lattice properties of stochastic orderings. We also identify properties of dependence structures leading to the minimal optimal stopping value. In the proofs we need an extension of Strassen's theorem on representation of the convex order which reveals that convex ordered distributions can be coupled by a two-step martingale (X,Y) with the additional property that Y is stochastically increasing in X.

Archimedean copulas, exchangeability, and max-stability

1994 ◽  
Vol 31 (2) ◽  
pp. 383-390 ◽  
Author(s):  
Rocco Ballerini
Keyword(s):  
Random Variables ◽  
Distribution Functions ◽  
Archimedean Copula ◽  
Archimedean Copulas ◽  
Monotone Transformation ◽  
Stable Property ◽  
Finite Dimensional ◽  
Finite Dimensional Distribution ◽  
Exchangeable Sequence ◽  
Dimensional Distribution

An exchangeable sequence of random variables is constructed with all finite-dimensional distribution functions having an Archimedean copula (as defined by Schweizer and Sklar (1983)). Through a monotone transformation of this exchangeable sequence, we obtain and characterize the class of exchangeable sequences possessing the max-stable property as defined by De Haan and Rachev (1989). Several parametric examples are given.

On the optimal stopping values induced by general dependence structures

2001 ◽  
Vol 38 (03) ◽  
pp. 672-684 ◽  
Author(s):  
Alfred Müller ◽  
Ludger Rüschendorf
Keyword(s):  
Optimal Stopping ◽  
Random Variables ◽  
Dependence Structure ◽  
Optimal Stopping Problem ◽  
Convex Order ◽  
Joint Distribution Function ◽  
Positive Dependence ◽  
Joint Distributions ◽  
Dependence Structures

The optimal stopping value of random variables X 1,…,X n depends on the joint distribution function of the random variables and hence on their marginals as well as on their dependence structure. The maximal and minimal values of the optimal stopping problem is determined within the class of all joint distributions with fixed marginals F 1,…,F n . They correspond to some sort of strong negative or positive dependence of the random variables. Any value inbetween these two extremes is attained for some dependence structures. The determination of the minimal value is based on some new ordering results for probability measures, in particular on lattice properties of stochastic orderings. We also identify properties of dependence structures leading to the minimal optimal stopping value. In the proofs we need an extension of Strassen's theorem on representation of the convex order which reveals that convex ordered distributions can be coupled by a two-step martingale (X,Y) with the additional property that Y is stochastically increasing in X.

scholarly journals A Study on Modelling of Bivariate Competing Risks with Archimedean Copulas

2021 ◽  
pp. 14-21
Author(s):  
Cigdem Topcu Guloksuz
Keyword(s):  
Competing Risks ◽  
Distribution Functions ◽  
Archimedean Copula ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Failure Times ◽  
Specific Distribution ◽  
Independent Censoring ◽  
Set Up ◽  
Best Fit

In this study we consider Archimedean copula functions to obtain estimates of cause-specific distribution functions in bivariate competing risks set up. We assume that two failure times of the same group are dependent and this dependency can be modeled by an Archimedean copula. Based on the Archimedean copula which gives best fit to the competing risk data with independent censoring we obtain the estimates of cause specific sub distributions.

Archimedean copulas, exchangeability, and max-stability

1994 ◽  
Vol 31 (02) ◽  
pp. 383-390 ◽  
Author(s):  
Rocco Ballerini
Keyword(s):  
Random Variables ◽  
Distribution Functions ◽  
Archimedean Copula ◽  
Archimedean Copulas ◽  
Monotone Transformation ◽  
Stable Property ◽  
Finite Dimensional ◽  
Finite Dimensional Distribution ◽  
Exchangeable Sequence ◽  
Dimensional Distribution

An exchangeable sequence of random variables is constructed with all finite-dimensional distribution functions having an Archimedean copula (as defined by Schweizer and Sklar (1983)). Through a monotone transformation of this exchangeable sequence, we obtain and characterize the class of exchangeable sequences possessing the max-stable property as defined by De Haan and Rachev (1989). Several parametric examples are given.

Dependence structure between money and economic activity: A Markov-switching copula VEC approach

2021 ◽  
pp. 1-17
Author(s):  
Apostolos Serletis ◽  
Libo Xu
Keyword(s):  
Error Correction ◽  
Economic Activity ◽  
Regime Switching ◽  
Markov Switching ◽  
Tail Dependence ◽  
Error Correction Model ◽  
Dependence Structure ◽  
Copula Models ◽  
Correction Model ◽  
Dependence Structures

Abstract This paper examines correlation and dependence structures between money and the level of economic activity in the USA in the context of a Markov-switching copula vector error correction model. We use the error correction model to focus on the short-run dynamics between money and output while accounting for their long-run equilibrium relationship. We use the Markov regime-switching model to account for instabilities in the relationship between money and output, and also consider different copula models with different dependence structures to investigate (upper and lower) tail dependence.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

MODELING DEPENDENCE BETWEEN LOSS TRIANGLES WITH HIERARCHICAL ARCHIMEDEAN COPULAS

2015 ◽  
Vol 45 (3) ◽  
pp. 577-599 ◽  
Author(s):  
Anas Abdallah ◽  
Jean-Philippe Boucher ◽  
Hélène Cossette
Keyword(s):  
Life Insurance ◽  
Bootstrap Method ◽  
Dependence Structure ◽  
Insurance Company ◽  
Archimedean Copulas ◽  
Life Insurance Company ◽  
Critical Problems ◽  
Intuitive Interpretation ◽  
Property Casualty

AbstractOne of the most critical problems in property/casualty insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. Recently, Shi and Frees (2011) proposed to put dependence between lines of business with a copula that captures dependence between two cells of two different runoff triangles. In this paper, we propose to generalize this model in two steps. First, by using an idea proposed by Barnett and Zehnwirth (1998), we will suppose a dependence between all the observations that belong to the same calendar year (CY) for each line of business. Thereafter, we will then suppose another dependence structure that links the CYs of different lines of business. This model is done by using hierarchical Archimedean copulas. We show that the model provides more flexibility than existing models, and offers a better, more realistic and more intuitive interpretation of the dependence between the lines of business. For illustration, the model is applied to a dataset from a major US property-casualty insurer, where a bootstrap method is proposed to estimate the distribution of the reserve.

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