Results and DiscussionIn this paper, we evaluate the CoVaR for BB1, BB6, BB7, and BB8 Copula functions and, based on this, estimate the CoES in ARMA-GARCH models with GED errors.Finally, these two criteria are calculated with the returns of Bank Tejarat and Bank Mellat. ConclusionIn this paper, essential methods for examining systemic risk, namely Conditional Value at Risk and Conditional Expected Shortfall, were studied based on Archimedean Copula functions BB1, BB6, BB7, and BB8 and ARMA-GARCH time series models with Generalized Error Distribution.Finally, this criterion was calculated for Bank Mellat if Bank Tejarat is in a critical situation.Finally, this criterion was calculated for Bank Mellat, assuming Bank Tejarat is in a crucial situation.To examine the dependence structure between these two returns and to predict Bank Mellat's future volatility, different Copula functions were used, and GARCH and ARMA-GARCH time series models were employed.The results indicated that the copula BB8 and the time series AR(1) -GARCH(1, 1) provide the best modeling.

The prevalence of high-dimensional datasets has driven increased utilization of the penalized likelihood methods. However, when the number of observations is relatively few compared to the number of covariates, each observation can tremendously influence model selection and inference. Therefore, identifying and assessing influential observations is vital in penalized methods. This article reviews measures of influence for detecting influential observations in high-dimensional lasso regression and has recently been introduced. Then, these measures under the elastic net method, which combines removing from lasso and reducing the ridge coefficients to improve the model predictions, are investigated. Through simulation and real datasets, illustrate that introduced influence measures effectively identify influential observations and can help reveal otherwise hidden relationships in the data.

IntroutionThe population multiple correlation coefficient (PMCC) measures the correlation between a given one-dimensional random variable X and multidimensional random vector X .This measure is the maximum correlation between X and any linear combination of components X .Testing the null hypothesis of zero PMCC is the most favourable approach to investigate the existence or non-existence of PMCC between X and X .The classical procedures for testing this hypothesis in high-dimensional data settings are invalid since the sample covariance matrix inverse or sample precision matrix is undefined.To cope with this problem, a simple test is constructed for testing zero PMCC in high-dimensional normal data.A small simulation study was carried out to evaluate the performance of the proposed test in both high-dimensional and low-dimensional normal data sets.Finally, the proposed test is applied to mice tumour volumes data. ateria an ethosThe proposed test includes the following two steps: In the first step, using a plug-in estimator of the sample precision matrix, a simple test statistic, called plug-in test statistic, was derived which uses the EQUALs method (Wang and Jiang, ) to estimate the precision matrix.In the second step, a permutation test is constructed using the proposed plug-in statistic to test the null hypothesis of zero PMCC.Theoretical investigations demonstrate that the proposed testing procedure is a level test. . . . . .