On the dependence structure of hitting times of multivariate processes

1989 ◽  
Vol 26 (2) ◽  
pp. 287-295 ◽  
Author(s):  
Nader Ebrahimi ◽  
T. Ramallingam
Keyword(s):  
Direct Approach ◽  
Hitting Times ◽  
Dependence Structure ◽  
Negative Dependence ◽  
Multivariate Processes ◽  
Positive And Negative Dependence ◽  
Dependence Properties ◽  
Dependence Structures

A direct approach to derive dependence properties among the hitting times of bivariate processes has been initiated by Ebrahimi (1987) and explored further by Ebrahimi and Ramallingam (1988). In this paper, new results are obtained for multivariate processes, which help us to identify positive and negative dependence structures among the hitting times of the processes. Applications of our theorems to reliability of systems are given.

On the dependence structure of hitting times of multivariate processes

1989 ◽  
Vol 26 (02) ◽  
pp. 287-295
Author(s):  
Nader Ebrahimi ◽  
T. Ramallingam
Keyword(s):  
Direct Approach ◽  
Hitting Times ◽  
Dependence Structure ◽  
Negative Dependence ◽  
Multivariate Processes ◽  
Positive And Negative Dependence ◽  
Dependence Properties ◽  
Dependence Structures

A direct approach to derive dependence properties among the hitting times of bivariate processes has been initiated by Ebrahimi (1987) and explored further by Ebrahimi and Ramallingam (1988). In this paper, new results are obtained for multivariate processes, which help us to identify positive and negative dependence structures among the hitting times of the processes. Applications of our theorems to reliability of systems 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.

scholarly journals Application of Copula functions in statistics

2007 ◽  
Author(s):  
Αριστείδης Νικολουλόπουλος
Keyword(s):  
Discrete Data ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Multivariate Distribution ◽  
Dependence Structure ◽  
Copula Models ◽  
Cumulative Distribution Functions ◽  
Multivariate Discrete Distributions ◽  
Dependence Properties ◽  
Multivariate Copula

Studying associations among multivariate outcomes is an interesting problem in statistical science. The dependence between random variables is completely described by their multivariate distribution. When the multivariate distribution has a simple form, standard methods can be used to make inference. On the other hand one may create multivariate distributions based on particular assumptions, limiting thus their use. Unfortunately, these limitations occur very often when working with multivariate discrete distributions. Some multivariate discrete distributions used in practice can have only certain properties, as for example they allow only for positive dependence or they can have marginal distributions of a given form. To solve this problem copulas seem to be a promising solution. Copulas are a currently fashionable way to model multivariate data as they account for the dependence structure and provide a flexible representation of the multivariate distribution. Furthermore, for copulas the dependence properties can be separated from their marginal properties and multivariate models with marginal densities of arbitrary form can be constructed, allowing a wide range of possible association structures. In fact they allow for flexible dependence modelling, different from assuming simple linear correlation structures. However, in the application of copulas to discrete data marginal parameters affect dependence structure, too, and, hence the dependence properties are not fully separated from the marginal properties. Introducing covariates to describe the dependence by modelling the copula parameters is of special interest in this thesis. Thus, covariate information can describe the dependence either indirectly through the marginalparameters or directly through the parameters of the copula . We examine the case when the covariates are used both in marginal and/or copula parameters aiming at creating a highly flexible model producing very elegant dependence structures. Furthermore, the literature contains many theoretical results and families of copulas with several properties but there are few papers that compare the copula families and discuss model selection issues among candidate copula models rendering the question of which copulas are appropriate and whether we are able, from real data, to select the true copula that generated the data, among a series of candidates with, perhaps, very similar dependence properties. We examined a large set of candidate copula families taking intoaccount properties like concordance and tail dependence. The comparison is made theoretically using Kullback-Leibler distances between them. We have selected this distance because it has a nice relationship with log-likelihood and thus it can provide interesting insight on the likelihood based procedures used in practice. Furthermore a goodness of fit test based on Mahalanobisdistance, which is computed through parametric bootstrap, will be provided. Moreover we adopt a model averaging approach on copula modelling, based on the non-parametric bootstrap. Our intention is not to underestimate variability but add some additional variability induced by model selection making the precision of the estimate unconditional on the selected model. Moreover our estimates are synthesize from several different candidate copula models and thus they can have a flexible dependence structure. Taking under consideration the extended literature of copula for multivariate continuous data we concentrated our interest on fitting copulas on multivariate discrete data. The applications of multivariate copula models for discrete data are limited. Usually we have to trade off between models with limited dependence (e.g. only positive association) and models with flexible dependence but computational intractabilities. For example, the elliptical copulas provide a wide range of flexible dependence, but do not have closed form cumulative distribution functions. Thus one needs to evaluate the multivariate copula and, hence, a multivariate integral repeatedly for a large number of times. This can be time consuming but also, because of the numerical approach used to evaluate a multivariate integral, it may produce roundoff errors. On the other hand, multivariate Archimedean copulas, partially-symmetric m-variate copulas with m − 1 dependence parameters and copulas that are mixtures of max-infinitely divisible bivariate copulas have closed form cumulative distribution functions and thus computations are easy, but allow only positive dependence among the random variables. The bridge of the two above-mentioned problems might be the definition of a copula family which has simple form for its distribution function while allowing for negative dependence among the variables. We define such a multivariate copula family exploiting the use of finite mixture of simple uncorrelated normal distributions. Since the correlation vanishes, the cumulative distribution is simply the product of univariate normal cumulative distribution functions. The mixing operation introduces dependence. Hence we obtain a kind of flexible dependence, and allow for negative dependence.

scholarly journals Multivariate Eulerian Polynomials and Exclusion Processes

2016 ◽  
Vol 25 (4) ◽  
pp. 486-499 ◽  
Author(s):  
P. BRÄNDÉN ◽  
M. LEANDER ◽  
M. VISONTAI
Keyword(s):  
Finite Number ◽  
Exclusion Process ◽  
Partition Functions ◽  
Asymmetric Exclusion Process ◽  
Negative Dependence ◽  
Combinatorial Interpretation ◽  
Exclusion Processes ◽  
Eulerian Polynomials ◽  
The Third ◽  
Dependence Properties

We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and coloured permutations. The corresponding expressions of the multivariate partition functions are then related to multivariate generalisations of Eulerian polynomials for coloured permutations considered recently by N. Williams and the third author, and others. We also discuss stability and negative dependence properties satisfied by the partition functions.

Exploring dependence structures in the international arms trade network: A network autocorrelation approach

2019 ◽  
Vol 20 (2) ◽  
pp. 195-218 ◽  
Author(s):  
Michael Lebacher ◽  
Paul W Thurner ◽  
Göran Kauermann
Keyword(s):  
Spatial Econometrics ◽  
Trade Flow ◽  
Information Criterion ◽  
Trade Flows ◽  
Dependence Structure ◽  
Network Autocorrelation ◽  
Arms Trade ◽  
Disturbance Model ◽  
The Impact ◽  
Dependence Structures

In this article, we analyse dependence structures among international trade flows of major conventional weapons from 1952 to 2016. We employ a Network Disturbance Model commonly used in inferential network analysis and spatial econometrics. The dependence structure is represented by pre-defined weight matrices that allow for correlating flows from the network of international arms exchange. Three dependence structures are proposed, representing sender-, receiver- and sender–receiver-related dependencies. The appropriateness of the presumed structures is comparatively assessed using the Akaike Information Criterion (AIC). It turns out that the dependence structure among the arms trade flows is complex and can be represented best by a specification that relates each arms trade flow to all exports and imports of the sending and the receiving state. Controlling for exogenous variables, we find that the trade volume increases with the GDP of the sending and the receiving state while the impact of geographical distance, regime dissimilarity and formal alliance membership is rather small.

On the dependence structure of hitting times of univariate processes

1988 ◽  
Vol 25 (02) ◽  
pp. 355-362 ◽  
Author(s):  
Nader Ebrahimi ◽  
T. Ramalingam
Keyword(s):  
Brownian Motion ◽  
Structural Properties ◽  
Hitting Times ◽  
Dependence Structure ◽  
Special Case ◽  
New Better Than Used ◽  
Better Than

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

scholarly journals Technical note: Changes in cross- and auto-dependence structures in climate projections of daily precipitation and their sensitivity to outliers

2019 ◽  
Vol 23 (3) ◽  
pp. 1741-1749
Author(s):  
Jan Hnilica ◽  
Martin Hanel ◽  
Vladimír Puš
Keyword(s):  
Statistical Downscaling ◽  
Climate Model ◽  
Daily Precipitation ◽  
Global Climate Models ◽  
Dependence Structure ◽  
Climate Projections ◽  
Model Simulations ◽  
Correlation Structures ◽  
Climate Model Simulations ◽  
Dependence Structures

Abstract. Simulations of regional or global climate models are often used for climate change impact assessment. To eliminate systematic errors, which are inherent to all climate model simulations, a number of post-processing (statistical downscaling) methods have been proposed recently. In addition to basic statistical properties of simulated variables, some of these methods also consider a dependence structure between or within variables. In the present paper we assess the changes in cross- and auto-correlation structures of daily precipitation in six regional climate model simulations. In addition the effect of outliers is explored making a distinction between ordinary outliers (i.e. values exceptionally small or large) and dependence outliers (values deviating from dependence structures). It is demonstrated that correlation estimates can be strongly influenced by a few outliers even in large datasets. In turn, any statistical downscaling method relying on sample correlation can therefore provide misleading results. An exploratory procedure is proposed to detect the dependence outliers in multivariate data and to quantify their impact on correlation structures.

Aspects of Negative Dependence Structures

2013 ◽  
Vol 42 (5) ◽  
pp. 907-917
Author(s):  
M. Amini ◽  
H. R. Nili Sani ◽  
A. Bozorgnia
Keyword(s):  
Negative Dependence ◽  
Dependence Structures
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