In this study, we discuss the problem in measuring the risk in a portfolio based on value at risk (VaR) using asymmetric GJR-GARCH Copula. The approach based on the consideration that the assumption of normality over time for the return can not be fulfilled, and there is non-linear correlation for dependent model structure among the variables that lead to the estimated VaR be inaccurate. Moreover, the leverage effect also causes the asymmetric effect of dynamic variance and shows the weakness of the GARCH models due to its symmetrical effect on conditional variance. Asymmetric GJR-GARCH models are used to filter the margins while the Copulas are used to link them together into a multivariate distribution. Then, we use copulas to construct flexible multivariate distributions with different marginal and dependence structure, which is led to portfolio joint distribution does not depend on the assumptions of normality and linear correlation. VaR obtained by the analysis with confidence level 95% is 0.005586. This VaR derived from the best Copula model, t-student Copula with marginal distribution of t distribution.

The modeling of spatio-temporal processes is crucial in many fields such as environmental science, hydrology, and water storage engineering. A basic concept of the spatio-temporal model is an auto-covariance function. The stream network model based on the Euclidean distance as the auto-covariance function for investigating river pollution will potentially face a serious accuracy problem, due to the material or water pollutant movement on the water only occurring within the river network and the distance travelled not following the path of the river network. The use of the hydrologic distance may overcome the problem because, statistically, the Euclidean distance-based auto-covariance function is not valid if it is a negative-definite. Therefore, this study develops a spatio-temporal model of the generalized product–sum based on the hydrologic distance with a positive-definite property. The proposed model is built and, subsequently, it is then verified mathematically to be positive-definite. Furthermore, the relationships between the hydrologic distance, the Euclidean distance, and spatial configurations are also investigated. The simulation study result shows the proposed spatio-temporal model is positive-definite for some semivariogram models. The relationships between spatial configurations in the stream network follow an exponential model.

The accuracy of financial risk management involving a large number of assets is needed, but information about dependencies among assets cannot be adequately analyzed. To analyze dependencies on a number of assets, several tools have been added to standard multivariate copula. However, these tools have not been adequately used in apps with higher dimensions. The bivariate parametric copula families can be used to solve it. The multivariate copula can be built from the bivariate parametric copula which is connected by a graphical representation to become Pair Copula Constructions (PCCs) or vine copula. The application of C-vine and D-vine copula have been used in some researches, but the use of C-vine and D-vine copula is more limited than R-vine copula. Therefore, this study used R-vine copula to provide flexibility for modeling complex dependencies on a high dimension. Since copula is a static model, while stock values change over time, then copula should be combined with the ARMA- GARCH model for modeling the movement of shares (volatility). The objective of this paper is to select and estimate R-vine copula which is used to analyze PT Jasa Marga (Persero) Tbk (JSMR), PT Waskita Karya (Persero) Tbk (WSKT), and PT Bank Mandiri (Persero) Tbk (BMRI) from august 31, 2014 to august 31, 2017. From the method it is obtained that the selected copulas for 2 edges at the first tree are survival Gumbel and the copula for edge at the second tree is Gaussian.

In the last two decades, the number of model developments in the field of Geostatistics increased rapidly, especially in the Spatio-temporal models. Almost of these models are based on Euclidean distance, only a few which based on non-Euclidean distance. The purpose of this study is to analyze and visualize the types of literatures on stationary Spatio-temporal models that utilize General Product-sum and Hydrological distance through bibliometric analysis methods, by considering a set of bibliometric metrics, including productive and impact measures, methods analysis, and co-authorships analysis. Scientific research works related to Spatio-temporal models using the product-sum field that consider hydrological aspects, published between 2002 and 2022 are reviewed. Some of the most relevant research works in this field and some of the newest trends are collected during September 2022 from Google Scholar, Scopus and Dimensions databases. The literature search method is carried out in two steps. Firstly, literature sources were obtained from Google Scholar, Scopus and Dimensions. Secondly, meta-analysis is performed using Harzing's Publish or Perish and VOSviewer software program. Total of 488 articles related to Spatio-temporal product-sum, and 8 articles related to Spatio-temporal product-sum based on hydrologic distance are selected. The analysis result shows that the proposed topic “Spatio-temporal model using product-sum based on hydrologic distance” has a different significant attribute from the existing research works, i.e., the hydrologic distance. Therefore, the proposed topic can be considered has a novelty.