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The purpose of this paper is to explore the relationship between multivariate process capability indices and loss functions for both nominal‐the‐best and smaller‐the‐better cases, so the likelihood and consequences resulting from the nonconforming of a manufacturing process or an environmental system can be evaluated simultaneously.

In this paper, the authors present a new approach of correlated risk assessment by linking the multiple process capability indices and loss functions, in which the multivariate process capability indices and multivariate loss functions describe the likelihood and consequences as a result of nonconformities in multivariate manufacturing or environmental system, respectively. Then, the associated relationship equations are developed using multivariate methods. Moreover, a step‐by‐step procedure is provided to facilitate the implementation of the correlated risk assessment.

Given the multivariate process capability indices, the authors show that the expected loss can be estimated by developed relationship equations and two numerical examples are also given, to demonstrate how the correlated manufacturing and environmental risks can be properly assessed by linking the multivariate process capability indices and multivariate loss function.

The risk information of likelihood and expected loss, classified in the four planning zones of a strategic planning matrix, provides practising managers and engineers with a decision‐making tool for prioritizing their quality improvement projects when conducting risk assessment for any multivariate process or environmental system.

Once the existing quality/environmental problems and their Key Performance Indicators are identified, one may conduct risk assessment by applying the relationship equations to evaluate the impact of correlated risk on manufacturing processes or multiple environmental emissions inside company; this can lead to the direction of continuous improvement for any industry.

We consider the Bayes estimation of a multivariate sample selection model with p pairs of selection and outcome variables. Each of the variables may be discrete or continuous with a parametric marginal distribution, and their dependence structure is modeled through a Gaussian copula function. Markov chain Monte Carlo methods are used to simulate from the posterior distribution of interest. The methods are illustrated in a simulation study and an application from transportation economics.

The purpose of this paper is to show that multivariate t-distribution assumption provides a better description of stock return data than multivariate normality assumption.

The EM algorithm is applied to solve the statistical estimation problem almost analytically, and the asymptotic theory is provided for inference.

The authors find that the multivariate normality assumption is almost always rejected by real stock return data, while the multivariate t-distribution assumption can often be adequate. Conclusions under normality vs under t can be drastically different for estimating expected returns and Jensen’s αs, and for testing asset pricing models.

The results provide improved estimates of cost of capital and asset moment parameters that are useful for corporate project evaluation and portfolio management.

The authors proposed new procedures that makes it easy to use a multivariate t-distribution, which models well the data, as a simple and viable alternative in practice to examine the robustness of many existing results.

Purpose – In this chapter, copula theory is used to model dependence structure between hedge fund returns series.

Methodology/approach – Goodness-of-fit tests, based on the Kendall's functions, are applied as selection criteria of the “best” copula. After estimating the parametric copula that best fits the used data, we apply previous results to construct the cumulative distribution functions of the equally weighted portfolios.

Findings – The empirical validation shows that copula clearly allows better estimation of portfolio returns including hedge funds. The three studied portfolios reject the assumption of multivariate normality of returns. The chosen structure is often of Student type when only indices are considered. In the case of portfolios composed by only hedge funds, the dependence structure is of Franck type.

Originality/value of the chapter – Introducing goodness-of-fit bootstrap method to validate the choice of the best structure of dependence is relevant for hedge fund portfolios. Copulas would be introduced to provide better estimations of performance measures.

This research provides some evidence by the vine copula approach, suggesting the significant and symmetric causal relation between subsections of Baltic Exchange and hence concluding that investing in different indexes, which is currently a risk diversification system, is not a correct risk reduction strategy.

The daily observations of Baltic Capesize Index (BCI), Baltic Handysize Index (BHSI), Baltic Dirty Tanker Index (BDTI) and Baltic LNG Tanker Index (BLNG) over an eight-year period have been used. After collecting data, calculating the return and estimating the marginal distribution of return rates for each of the indexes applying asymmetric power generalized autoregressive conditional heteroskedasticity and autoregressive moving average (APGARCH-ARMA), and with the assumption of skew student's t-distribution, the dependence of Baltic indexes was modeled based on Vine-R structures.

A positive and symmetrical correlation was observed between the study groups. High and low tail dependence is observed between all four indexes. In other words, the sector business groups associated with each of these indexes react similarly to the extreme events of other groups. The BHSI has a pivotal role in examining the dependency structure of Baltic Exchange indexes. That is, in addition to the direct dependence of Baltic groups, the dependence of each group on the BHSI can transmit accidents and shocks to other groups.

Since the Baltic Exchange indexes are tradable, these findings have implications for portfolio design and hedging strategies for investors in shipping markets.

Vine copula structures proves the causal relationship between different Baltic Exchange indexes, which are derived from different types of markets.

We consider a semiparametric panel stochastic frontier model where one-sided firm effects representing inefficiencies are correlated with the regressors. A form of the Chamberlain-Mundlak device is used to relate the logarithm of the effects to the regressors resulting in a lognormal distribution for the effects. The function describing the technology is modeled nonparametrically using penalized splines. Both Bayesian and non-Bayesian approaches to estimation are considered, with an emphasis on Bayesian estimation. A Monte Carlo experiment is used to investigate the consequences of ignoring correlation between the effects and the regressors, and choosing the wrong functional form for the technology.

This paper aims to capture tail dependence between sentiment index and Shanghai composite index (SCI) by proposing a sentiment index based on text mining.

Online text mining and the Copula model were used in this study.

First, the paper finds herding effect in the expression of investors’ sentiment from online text data, and the usage occurrence frequency of most vocabulary is less correlative with SCI. Second, given these two features, the paper uses weighted divide-and-conquer algorithm to construct a sentiment index. Finally, because of multivariate non-Gaussian joint distribution between them, the paper uses the Copula model to detect their tail dependences, and finds that both upper and lower tail dependences could have a significant influence between positive sentiment and SCI, with a higher probability on the upper one. Additionally, only the upper tail dependence exhibits the significant influence between negative sentiment and SCI.

This paper proposes a framework of constructing investment sentiment index with the weighted conquer-and-divide algorithm, and characterizes tail dependence between sentiment index and SCI. The implication can measure the environment of investment market of China and provide an empirical ground for bandwagon effect and bargain shopper effect.

The purpose of this paper is to analyse the dependence structure in volatility between Shanghai and Shenzhen stock market in China based on high-frequency data.

Using a multiplicative error model (hereinafter MEM) to describe the margins in volatility of China’s Shanghai and Shenzhen stock market, this study adopts static and time-varying copulas, respectively, estimated by maximum likelihood estimation method to describe the dependence structure in volatility between Shanghai and Shenzhen stock market in China.

This paper has identified the asymmetrical dependence structure in financial market volatility more precisely. Gumbel copula could best fit the empirical distribution as it can capture the relatively high dependence degree in the upper tail part corresponding to the period of volatile price fluctuation in both static and dynamic view.

Previous scholars mostly use GARCH model to describe the margins for price volatility. As MEM can efficiently characterize the volatility estimators, this paper uses MEM to model the margins for the market volatility directly based on high-frequency data, and proposes a proper distribution for the innovation in the marginal models. Then we could use copula-MEM other than copula-GARCH model to study on the dependence structure in volatility between Shanghai and Shenzhen stock market in China from a microstructural perspective.

The purpose of this paper is to analyze the optimal hedging strategy of the oil-stock dependence structure.

The methodology consists to model the data over the daily period spanning from January 02, 2002 to May 19, 2016 by a various copula functions to better modeling the dependence between crude oil market and stock markets, and to use dependence coefficients and conditional variance to calculate optimal portfolio weights and optimal hedge ratios, and to suggest the best hedging strategy for oil-stock portfolio.

The findings show that the Gumbel copula is the best model for modeling the conditional dependence structure of the oil and stock markets in most cases. They also indicate that the best hedging strategy for oil price by stock market varies considerably over time, but this variation depends on both the index introduced and the model used. However, the conditional copula method with skewed student more effective than the other models to minimize the risk of oil-stock portfolio.

This research implication can be valuable for portfolio managers and individual investors who seek to make earnings by diversifying their portfolios. The findings of this study provide evidence of the importance of stock assets for making an optimal portfolio consisting of oil in the case of investments in oil and stock markets. This paper attempts to fill the voids in the literature on volatility among oil prices and stock markets in two important areas. First, it uses copulas to investigate the conditional dependence structure of the oil crude and stock markets in the oil exporting and importing countries. Second, it uses the dependence coefficients and conditional variance to calculate dynamic hedge ratios and risk-minimizing optimal portfolio weights for oil–stock.

We consider conditional distribution and conditional density functionals in the space of generalized functions. The approach follows Phillips (1985, 1991, 1995) who employed generalized functions to overcome non-differentiability in order to develop expansions. We obtain the limit of the kernel estimators for weakly dependent data, even under non-differentiability of the distribution function; the limit Gaussian process is characterized as a stochastic random functional (random generalized function) on the suitable function space. An alternative simple to compute estimator based on the empirical distribution function is proposed for the generalized random functional. For test statistics based on this estimator, limit properties are established. A Monte Carlo experiment demonstrates good finite sample performance of the statistics for testing logit and probit specification in binary choice models.