A comprehensive comparison of copula models and multivariate normal distribution for geo-material parametric data

Bayesian Approaches to Copula Modelling

PurposeThe purpose of this paper is to provide an analysis of the dependence structure between returns from real estate investment trusts (REITS) and a stock market index. Further, the aim is to illustrate how copula approaches can be applied to model the complex dependence structure between the assets and for risk measurement of a portfolio containing investments in REIT and equity indices.Design/methodology/approachThe usually suggested multivariate normal or variance‐ covariance approach is applied, as well as various copula models in order to investigate the dependence structure between returns of Australian REITS and the Australian stock market. Different models including the Gaussian, Studentt, Clayton and Gumbel copula are estimated and goodness‐of‐fit tests are conducted. For the return series, both the Gaussian and a non‐parametric estimate of the distribution is applied. A risk analysis is provided based on Monte Carlo simulations for the different models. The value‐at‐risk measure is also applied for quantification of the risks for a portfolio combining investments in real estate and stock markets.FindingsThe findings suggest that the multivariate normal model is not appropriate to measure the complex dependence structure between the returns of the two asset classes. Instead, a model using non‐parametric estimates for the return series in combination with a Studenttcopula is clearly more suitable. It further illustrates that the usually applied variance‐covariance approach leads to a significant underestimation of the actual risk for a portfolio consisting of investments in REITS and equity indices. The nature of risk is better captured by the suggested copula models.Originality/valueTo the authors', knowledge, this is one of the first studies to apply and test different copula models in real estate markets. Results help international investors and portfolio managers to deepen their understanding of the dependence structure between returns from real estate and equity markets. Additionally, the results should be helpful for implementation of a more adequate risk management for portfolios containing investments in both REITS and equity indices.

Copulas have become an important analytic tool for characterizing multivariate distributions and dependence. One is often interested in simulating data from copula estimates. The process can be analytically and computationally complex and usually involves steps that are unique to a given parametric copula. We describe an alternative approach that uses \probability{proportional{to{size" (PPS) random sampling with weights formed from the copula likelihood function. The method is flexible and can be applied to parametric and nonparametric marginal density estimates. The precision of the simulation can be calibrated by adjusting the density of the multidimensional grid used in the simulation process. The approach is fully transparent to any copula function with continuous random variables. An example evaluates a number of goodness-of-fit criteria and provides strong support for the validity and practicality of the method.

Contemporary financial risk management is significantly based on the analysis of time series of returns. One of the most significant errors frequently committed by analysts is the predominant use of normal distributions when it is clear that the returns are not normal. Copula models and models for non-normal multivariate distributions provide new tools to solve the problem because the obtained results are immediately applicable in portfolio management, option pricing and measuring risk without assuming normality. Therefore, both a theoretician and a practitioner are interested in multivariate models for returns and copula functions. The copula function models provide an effective and interesting technique of constructing multivariate distribution starting from marginal ones. Due to Sklar\'s result established in 1959, we can present any multivariate distribution with a help of corresponding marginal distributions and a selected copula function. In this work we present an application of copula function to construct multivariate conditional distributions of times series. In the last part of this paper dynamic models such as DCC-MVGARCH and conditional copula are analyzed. Moreover, we also present an application of bootstrap in the context of copula function. This work is appended by examples showing practical application of our work.

Background Antenatal screening for Trisomy 21 (T21) in the UK is performed primarily in the first trimester. Nuchal Translucency (NT), gestational age, Free β-HCG and PAPP-A are used in combination, creating the ‘combined’ test. Multivariate Gaussian distribution models then determine the chance of T21 expressed as an odds ratio. This study investigates the use of machine-learning algorithms in the prediction of T21 in first-trimester singleton pregnancies and compares their performance to existing screening models. Methods A total of 86,354 anonymised, first trimester, singleton pregnancy screening cases, including 211 with T21, were used to train and test machine-learning models using adaptive boosting technology. Test case results were compared with pregnancy outcome data to assess performance. Results A machine-learning model was able to outperform current multivariate distribution models (McNemar’s p = .006, AUC 0.978 vs 0.974). False positive rates were reduced from 3.82% to 2.28% (95% CI: 3.56–4.08 and 2.08–2.48 respectively) and overall screen positive rates were reduced from 4.00% to 2.48% (95% CI: 3.74–4.28 and 2.27–2.70 respectively). Conclusions Machine-learning algorithms offer demonstrable improvements to first-trimester singleton T21 screening without major changes to the UK programme. Larger datasets and improved outcome data would likely offer further increases in performance.

SUMMARY The conditional predictive ordinate (CPO) is a Bayesian diagnostic which detects surprising observations. It has been used in a variety of situations such as univariate samples, the multivariate normal distribution and regression models. Results are presented about the most surprising observation which has minimum CPO. For the multivariate normal distribution it is shown that the most surprising observation must lie at one of the vertices of the convex hull. It is also shown that the observation with maximum Mahalanobis distance from the sample mean must lie on the convex hull. Results are given for the expected number of vertices on the convex hull when the sample is contaminated. An alternative, closely related diagnostic, the ratio ordinate measure, is presented. A numerical comparison of the two measures is given.

This paper aims to study the structure of interdependencies between the energy, biofuel and agricultural commodity markets. The work concentrates on the dependence between ethanol and agricultural futures returns conditional to crude oil returns, and interdependence among agricultural commodities conditional to crude oil and ethanol futures returns. The C-vine copula based ARMA-GARCH model was used to explain the dependence structure of crude oil and the four related variables, and applied to investigate the risk of energy-agricultural commodity futures portfolio.We generally found symmetry in the tail dependence between the energy, biofuel, and agricultural commodities, and also found a greater significant variability in dependence, specifically, the dependence between the ethanol and agricultural commodity futures returns conditional to crude oil as well as interdependence between corn and soybean conditional to crude oil and ethanol return. This indicates that there is a rise in ethanol productions and that higher crude oil prices have caused a price increase in agricultural commodities such as corn and soybean. Moreover, the higher dynamic dependence and symmetric tail dependences indicate that opportunities for portfolio diversification are reduced, particularly during a downturn in the markets. Finally, our result suggests that the time-varying copula model captures the portfolio risk better than the static copula models.

In this paper, we are interested in investigating the causal relationships among futures sugar prices in the Zhengzhou futures exchange market (ZF), the spot sugar prices in Zhengzhou (ZS) and the futures sugar prices in New York futures exchange market (NF). A useful tool called Bayesian network is introduced to analyze the problem. Since there are only three variables in our Bayesian network, the algorithm is straightforward: we display all the 25 possible network structures and adopt certain scoring metrics to evaluate them. We applied five different scoring metrics in total. Firstly, for each metric, we obtained 24 scores, each calculated from one of the 24 possible structures i.e. a Directed Acyclic Graph (DAG). Then we eliminated the network structure which represents the independence of the three variables according to our prior knowledge concerning the futures sugar market. After that, the optimal network structure which implies the causal relationships was selected according to the corresponding scoring metric. Finally, after comparing the results from different scoring metrics, we obtained the relatively affirmative conclusion that ZS causes ZF from both the Bayesian Dirichlet (BD) metric, Bayesian Dirichlet-Akaike Information Criterion (BD-AIC) metric, Bayesian Dirichlet-Bayesian Information Criterion (BD-BIC) metric and Bayesian Information Criterion (BIC) metric. The conclusions that NF causes ZF and ZF causes ZS from the Akaike Information Criterion (AIC) metric and ZF causes ZS from the BIC metric were useful and significant to our investigation.

The age and growth information of fish is important for assessment of the dynamics, planning, and management in fisheries. In this study, the mean size at age data of 10 fish species collected from literature were fitted by the five growth models and the growth parameters were estimated by the maximum likelihood method. The best model was selected using the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The growth of most species can be best described by the von Bertalanffy and allometric growth models. The results showed that both AIC and BIC have their advantages in the testing of significance of the difference between the functions of models. As for the demersal fishes (snappers and groupers), BIC is better than AIC in selecting the best growth model.

Daily scale streamflow forecasting in multiple stream orders of Cauvery River, India: Application of advanced ensemble and deep learning models

Small area statistics are required when the sample size is small to produce estimates with adequate precision. The assumptions underlying Battese Harter Fuller (BHF) unit-level models may often be unrealistic in some applications. Copula is an alternative approach when the assumptions are violated. This research discusses the performance of BHF and Copula in small area estimation (SAE) for estimating household per capita expenditure in sub-district levels. This study presents household per capita expenditure, which has a skewed distribution. Due to the fact that the data contains outliers, an appropriate method to handle outliers is also considered. In this research, the Gaussian and the Clayton Copulas are used. The results showed that the performance of BHF was better than Gaussian and Clayton Copulas, as indicated by small root mean square error (RMSE) with an average of 1.14, while the average RMSE of Gaussian copula was 2.71 and Clayton copula was 2.63. Furthermore, the coefficient of variation (CV) of BHF was also smaller compared to Gaussian and Clayton Copulas, and the resulting estimates can be categorized as reliable based on the CV of less than 25%.

Multivariate distribution models with generalized hyperbolic margins

Multivariate distributions with correlation matrices for nonlinear repeated measurements

The infectious coronavirus disease 2019 (COVID-19) has become a serious global pandemic. Different studies have shown that increasing temperature can play a crucial role in the spread of the virus. Most of these studies were limited to winter or moderate temperature levels and were conducted using conventional models. However, traditional models are too simplistic to investigate complex, non-linear relationships and suffer from some restrictions. Therefore, we employed copula models to examine the impact of high temperatures on virus transmission. The findings from the copula models showed that there was a weak to moderate effect of temperature on the number of infections and the effect almost vanished under a lockdown policy. Therefore, this study provides new insight into the relationship between COVID-19 and temperature, both with and without social isolation practices. Such results can lead to improvements in our understanding of this new virus. In particular, the results derived from the copula models examined here, unlike existing traditional models, provide evidence that there is no substantial influence of high temperatures on the active COVID-19 outbreak situation. In addition, the results indicate that the transmission of COVID-19 is strongly influenced by social isolation practices. To the best of the author knowledge, this is the first copula model investigation applied to the COVID-19 pandemic.

Time series study is of paramount importance especially in developing countries such as India. The objective of this study is to forecast the number of dengue cases by applying time series models. Furthermore, this study also aims to uncover the correlation of ecological variables with dengue cases using a p value test. The ecological variables considered are the rainfall (with a 2-month lag period) and average relative humidity. An evaluation of host factors such as age and gender is done with the number of cases to determine the most affected strata. Monthly data on dengue cases from 2014 to 2017 are taken from the integrated disease surveillance programme, Government of India, and data on ecological variables, humidity and rainfall are taken from www.Indiastat.com . A 2-month lag period is considered for rainfall. These data were analysed by the autoregressive integrated moving average (ARIMA) and exponential smoothing model (ES). Predictive performance of these techniques was assessed by evaluation parameters such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute error and mean absolute scaled error. Applying time series models was useful in the prediction. There were many more males than females according to the data for 2014–2017. The Akaike information criterion (AIC), Bayesian information criterion (BIC) and mean absolute scaled error for ARIMA are 48.6526, 448.333333, 449.30008, 453.08 and 0.507826, respectively. Based on model indices such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute error and mean absolute scaled error, the ARIMA performed better than the ES model. Rainfall at the 2-month lag was correlated with the number of cases.