Correlation Analysis of Influencing Factors and the Monthly Displacement Increment of a Hydrodynamic Landslide Using a Pseudo-Maximum-Likelihood-Estimation-Mixed-Copula Approach

Heavy rainfall and changes in the water levels of reservoirs directly affect the degree of landslide disasters in major hydropower project reservoir areas. Correlation analyses of rainfall- and water-level fluctuations with landslide displacement changes can provide a scientific basis for the prevention and early warning of landslide disasters in reservoir areas. Because of the shortcomings of the traditional correlation analysis based on linear assumptions, this study proposed the use of a pseudo-maximum-likelihood-estimation-mixed-Copula (MLE-M-Copula) method instead of linear assumptions. We used the Bazimen landslide in the Three Gorges Reservoir Area as a case study to carry out the correlation analysis of the rainfall, water-level fluctuations, and landslide displacement. First, we selected several appropriate influencing factors to construct four candidate Copula models and estimated the parameters using the pseudo-MLE method. After the goodness-of-fit test, we selected the M-Copula model as the optimal model and used this model to study correlations between the monthly displacement increment of the landslide and influencing factors. We then established the joint distribution functions of these correlations. We computed and analyzed the overall and tail correlations between the displacement increment and the influencing factors, and we constructed the conditional probability distribution of the monthly displacement increment for different given conditions. The results showed that the pseudo-MLE-M-Copula method effectively quantified the correlation between the rainfall, reservoir-level fluctuations, and landslide displacement changes, and we obtained the return periods and value at risk of the influencing factors of the Bazimen landslide under different rainfall conditions and reservoir-level changes. Furthermore, the tail correlations between the monthly displacement increment of the landslide and the rainfall- and reservoir-level changes were higher than the overall correlations.

Asymmetric COGARCH processes

Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time GARCH model, concentrating then on the GJR-COGARCH model. We calculate higher-order moments and extend the first-jump approximation. These results are prerequisites for moment estimation and pseudo maximum likelihood estimation of the GJR-COGARCH model parameters, respectively, which we derive in detail.