Time series copulas for heteroskedastic data

We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We suggest copulas for first‐order Markov series, and then extend them to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence, including co‐movement and spillover in multivariate series. In general, these depend upon the marginal distributions of the series. Using exchange rate returns, we show that the resulting copula models can capture their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models, and produce more accurate value‐at‐risk forecasts.     

A new extension of bivariate FGM copulas

We propose a new family of copulas generalizing the Farlie–Gumbel–Morgenstern family and generated by two univariate functions. The main feature of this family is to permit the modeling of high positive dependence. In particular, it is established that the range of the Spearman’s Rho is [ − 3/4,1] and that the upper tail dependence coefficient can reach any value in [0,1]. Necessary and sufficient conditions are given on the generating functions in order to obtain various dependence properties. Some examples of parametric subfamilies are provided.     

A method to obtain new copulas from a given one

Given a strictly increasing continuous function φ from [0, 1] to [0, 1] and its pseudo-inverse φ^[−1], conditions that φ must satisfy for C_φ(x₁, . . . ,x_n)=φ^[−1](C(φ(x₁), . . . ,φ(x_n))) to be a copula for any copula C are studied. Some basic properties of the copulas obtained in this way are analyzed and several examples of generator functions φ that can be used to construct copulas C_φ are presented. In this manner, a method to obtain from a given copula C a variety of new copulas is provided. This method generalizes that used to construct Archimedean copulas in which the original copula C is the product copula, and it is related with mixtures     

A model of vertical integration and investment in generation capacity in electricity markets: The case of the bidding game

The aim of this work is to assess the impact of (partial) vertical integration between generators and retailers on generation capacity choice and its subsequent welfare consequences. We present a framework in which final demand is perfectly inelastic and stochastic. Nevertheless, wholesale demand is elastic because of the existence of outside opportunities (mainly international transmission capacity). The model is a three-stage game. Neither transmission nor retail costs are taken into account.

In the first stage of the game, generators choose capacity only knowing distribution of demand and thus maximizing their expected profit. The second stage of the game represents the competition for market share between retailers in a market where consumers have switching costs. The former face unknown demand and maximize their utility based on two factors: the expected profit and a risk element. Finally, generators submit bid functions to the system operator given known demand and maximizing their profit during the last stage of the game. Retailers and generators interact in the wholesale market, which is cleared by the system operator whose function is to match supply (represented by the bids of the generators) and demand through a system of single price auctions. The wholesale market is the only means to buy and sell energy; there are no bilateral contracts between firms, except if they are vertically integrated.

We compare fully disintegrated and partially vertically integrated structures using a comparative statics approach. In this paper, the analysis will focus on the last stage of the game: the bidding game. We find that partial vertical integration between generators and retailers tends to lower wholesale prices but not unambiguously. Depending on which firm (vertically integrated or disintegrated generator) has installed the higher capacity and depending on level of demand, prices can stay unchanged or even rise.     

Large sample properties for a class of copulas in bivariate survival analysis

This work is concerned with asymptotic properties of the bivariate survival function estimator using the functional relationship between marginal survival functions and a class of copulas for the dependence structure. Specifically, we study consistency and weak convergence of the bivariate survival function estimator obtained considering a two-step procedure of estimation. The obtained results are found from a key decomposition of the bivariate survival function in quantities that can be studied separately. In particular, we use relating results to almost sure and weak convergence of estimators, almost sure convergence of uniformly equicontinuous functions, and the delta method for functionals.     

The t Copula and Related Copulas

The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively.     

Robustness of some non-uniform random variate generators

Often the usefulness of a random variate generator for a distribution is based on the successful generation of independent variates from the uniform distribution. However, no pseudo-random number generator is capable of generating a truly random uniform sequence. As the cost of computations is now dramatically reduced, the computational efficiency should not be the primary criterion in choosing a good generator. Proposed here is a robustness criterion which is designed to study the effect of an imperfect pseudo-random number generator on the accuracy of a random variate generator. In particular, the beta and binomial variate generators are examined for their robustness to the non-uniformity of a pseudo-random number generator.     

雾气发生器的研制

雾气发生器是模拟汽车风窗玻璃除霜除雾系统的必用设备,原有设备雾气排量已达不到新标准GB11555-2009要求,而且没有缺水系统保护、加热、定时、风扇及断水等指示显示,不便于试验工作的顺利进行。鉴于该情况,我们结合新标准对汽车风窗玻璃除霜除雾系统的要求,研制出新型、功能更齐全以及工作稳定性更高的雾气发生器。     

柴油发电机组的并联运行

阐述柴油发电机的并联运行的必要性,如何将不同型号、新老产品的发电机组并联运行,发电机组并联运行应满足的条件,发电机组并联运行操作步骤,调试中可能出现的问题,并对调试中出现的问题进行了解决。     

Classification and Discrimination Problems with Applications, Part IIa

Abstract  In Part I exact results for univariate (" p = 1") two-group ("k = 2") classification problems were derived assuming normality and equality of the variances. In Part IIa asymptotic results for multivariate (" p > I") two-group classification and discrimination problems are based on the corresponding assumptions of multivariate normality and equality of the covariance matrices. The results (4.6.5), (4.6.6) and (4.6.7) are believed to be new.
The asymptotic results in Section 4.6, together with results presented elsewhere in the literature, constitute the basis of various detailed proposals to deal with problems from actual statistical practice. Most of these proposals are modifications or specifications of existing ones. We shall pay some attention to (I) testing whether differences exist. But we are mainly interested in: (II) constructing a discriminant function, (III) assigning the individual under classification, and in (IV) constructing a confidence interval for "the" posterior probability that the individual under classification belongs to Population 2.
An important part in our theory is played by various techniques for selecting variables in discriminant analysis. The need for such techniques follows from Section 4.10. The consequences of building-in a selection technique are discussed in Section 4.12. One of our proposals motivates the theory presented in Chapter 3 and is mentioned here for that reason: employ a large part of the data, say 70%, in order to construct a discriminant function (via a selection of variables); by applying this function to the rest of the data, the exact univariate theory of Part I becomes of application. Part IIb will contain a chapter on applications.     

Modelling soccer matches using bivariate discrete distributions with general dependence structure

In this paper copulas are used to generate bivariate discrete distributions. These distributions are fitted to soccer data from the English Premier League. An interesting aspect of these data is that the primary variable of interest, the discrete pair shots-for and shots-against, exhibits negative dependence; thus, in particular, we apply bivariate Poisson-related distributions that allow such dependence. The paper focuses on Archimedian copulas, for which the dependence structure is fully determined by a one-dimensional projection that is invariant under marginal transformations. Diagnostic plots for copula fit based on this projection are adapted to deal with discrete variables. Covariates relating to within-match contributions such as numbers of passes and tackles are introduced to explain variability in shot outcomes. The results of this analysis would appear to support the notion that playing the 'beautiful game' is an effective strategy—more passes and crosses contribute to more effective play and more shots on the goal.     

防止发电机失磁进相引起过流保护误动作的研究

为了保证励磁系统电压稳定性,一些发电机是允许进相同步运行的,而随着电网系统的不断增大,系统的无功储备更加充足,这也为单个机组低励进相稳定运行提供了保证。文章分析了发电机失磁运行的特性,阐述了发电机失磁进相时的物理过程,以及导致过流保护误动作的原因,并结合南京梅山能源有限公司现有发电机失磁保护的现状,提出了具有可操作性的预防措施,提高了发电机过流保护的可靠性。     

防止发电机失磁进相引起过流保护误动作的研究

为了保证励磁系统电压稳定性,一些发电机是允许进相同步运行的,而随着电网系统的不断增大,系统的无功储备更加充足,这也为单个机组低励进相稳定运行提供了保证。文章分析了发电机失磁运行的特性,阐述了发电机失磁进相时的物理过程,以及导致过流保护误动作的原因,并结合南京梅山能源有限公司现有发电机失磁保护的现状,提出了具有可操作性的预防措施,提高了发电机过流保护的可靠性。     

A new family of dispersive orderings

In this paper we introduce a new family of univariate dispersion orderings which, under mild conditions, includes the weakly dispersive ordering as a particular case. Different properties of the new class of dispersion orderings are analyzed. Some connections with other univariate dispersion orderings are stated. Finally an application of the new family of dispersion orders to the field of genetics is developed.     

Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence

We consider nonparametric estimation of multivariate versions of Blomqvist’s beta, also known as the medial correlation coefficient. For a two-dimensional population, the sample version of Blomqvist’s beta describes the proportion of data which fall into the first or third quadrant of a two-way contingency table with cutting points being the sample medians. Asymptotic normality and strong consistency of the estimators are established by means of the empirical copula process, imposing weak conditions on the copula. Though the asymptotic variance takes a complicated form, we are able to derive explicit formulas for large families of copulas. For the copulas of elliptically contoured distributions we obtain a variance stabilizing transformation which is similar to Fisher’s z-transformation. This allows for an explicit construction of asymptotic confidence bands used for hypothesis testing and eases the analysis of asymptotic efficiency. The computational complexity of estimating Blomqvist’s beta corresponds to the sample size n, which is lower than the complexity of most competing dependence measures.      

Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks

Distance functions are gaining relevance as alternative representations of production technologies, with growing numbers of empirical applications being made in the productivity and efficiency field. Distance functions were initially defined on the input or output production possibility sets by Shephard (1953, 1970) and extended to a graph representation of the technology by Färe, Grosskopf and Lovell (1985) through their graph hyperbolic distance function. Since then, different techniques such as non parametric-DEA and parametric-SFA have been used to calculate these distance functions. However, in the latter case we know of no study in which the restriction to input or output orientation has been relaxed. What we propose is to overcome such restrictiveness on dimensionality by defining and estimating a parametric hyperbolic distance function which simultaneously allows for the maximum equiproportionate expansion of outputs and reduction of inputs. In particular, we introduce a translog hyperbolic specification that complies with the conventional properties that the hyperbolic distance function satisfies. Finally, to illustrate its applicability in efficiency analysis we implement it using a data set of Spanish savings banks.     

Copula-based multivariate GARCH model with uncorrelated dependent errors

Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conventional MGARCH model as a special case. The aim of this paper is to model MGARCH for non-normal multivariate distributions using copulas. We model the conditional correlation (by MGARCH) and the remaining dependence (by a copula) separately and simultaneously. We apply this idea to three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle [Engle, R.F., 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20, 339–350], the varying correlation (VC) model of Tse and Tsui [Tse, Y.K., Tsui, A.K., 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20, 351–362], and the BEKK model of Engle and Kroner [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150]. Empirical analysis with three foreign exchange rates indicates that the C-MGARCH models outperform DCC, VC, and BEKK in terms of in-sample model selection and out-of-sample multivariate density forecast, and in terms of these criteria the choice of copula functions is more important than the choice of the volatility models.     

Inversion copulas from nonlinear state space models with an application to inflation forecasting

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.     

A conditionally heteroskedastic independent factor model with an application to financial stock returns

We propose a new conditionally heteroskedastic factor model, the GICA-GARCH model, which combines independent component analysis (ICA) and multivariate GARCH (MGARCH) models. This model assumes that the data are generated by a set of underlying independent components (ICs) that capture the co-movements among the observations, which are assumed to be conditionally heteroskedastic. The GICA-GARCH model separates the estimation of the ICs from their fitting with a univariate ARMA-GARCH model. Here, we will use two ICA approaches to find the ICs: the first estimates the components, maximizing their non-Gaussianity, while the second exploits the temporal structure of the data. After estimating and identifying the common ICs, we fit a univariate GARCH model to each of them in order to estimate their univariate conditional variances. The GICA-GARCH model then provides a new framework for modelling the multivariate conditional heteroskedasticity in which we can explain and forecast the conditional covariances of the observations by modelling the univariate conditional variances of a few common ICs. We report some simulation experiments to show the ability of ICA to discover leading factors in a multivariate vector of financial data. Finally, we present an empirical application to the Madrid stock market, where we evaluate the forecasting performances of the GICA-GARCH and two additional factor GARCH models: the orthogonal GARCH and the conditionally uncorrelated components GARCH.     

Characterizations and Modelling of Multivariate Lack of Memory Property

In this article we establish characterizations of multivariate lack of memory property in terms of the hazard gradient (whenever exists), the survival function and the cumulative hazard function. Based on one of these characterizations we establish a method of generating bivariate lifetime distributions possessing bivariate lack of memory property (BLMP) with specified marginals. It is observed that the marginal distributions have to satisfy certain conditions to be stated. The method generates absolutely continuous bivariate distributions as well as those containing a singular component. Bivariate exponential distributions due to Proschan and Sullo (Reliability and biometry, pp 423–440, 1974), Freund (in J Am Stat Assoc 56:971–977, 1961), Block and Basu (J Am Stat Assoc 89:1091–1097, 1974) and Marshall and Olkin (J Am Math Assoc 62:30–44, 1967) are generated as particular cases among others using the proposed method. Some other distributions generated using the method may be of practical importance. Shock models leading to bivariate distributions possessing BLMP are given. Some closure properties of a class of univariate failure rate functions that can generate distributions possessing BLMP and of the class of bivariate survival functions having BLMP are studied.