Spatial Mixture Copula Model For Multiple Correlated Responses With An Environmental Application

In environmental monitoring, multiple measurements are often collected at many locations and these measurements depend on each other in complex ways, such as nonlinear dependence. In this research, a novel copula-based geostatistical modelling approach was developed to model multivariate continuous spatial random fields using mixture copulas that captures both spatial and joint dependence of multiple responses over two-dimensional locations. In a bivariate context, the mixture copulas were used to capture the joint spatial dependence of a bivariate random field and the spatial copula of the bivariate random field was constructed as the convex combination of mixture copulas. The proposed model was applied to real forest data and simulated nonlinear data. The performance of the novel method was compared with existing spatial methods, which included a univariate spatial pair-copula model, a multivariate spatial pair-copula model that utilises nonlinear principal component analysis (NLPCA), and conventional kriging. The results show that the proposed model outperforms the existing methods in the interpolation of individual responses and reproduction of their bivariate dependence.

Adoption of deep learning Markov model combined with copula function in portfolio risk measurement

In order to accurately describe the risk dependence structure and correlation between financial variables, carry out scientific financial risk assessment, and provide the basis for accurate financial decision-making, first the basic theory of Copula function is established and the mixed Copula model is constructed. Then the hybrid Copula model is nested in a hidden Markov model (HMM), the risk dependences among banking, insurance, securities and trust industries are analysed, and the Copula–Garch model is constructed for empirical analysis of investment portfolio. Finally, the deep learning Markov model is adopted to predict the financial index. The results show that the mixed Copula model based on HMM is more effective than the single Copula and the mixed Copula models. The empirical structure shows that among the four major financial industries in China, the banking and insurance industries have strong interdependence and high probability of risk contagion. The investment failure rate under 95%, 97.5% and 99% confidence intervals calculated by Copula–Garch model are 4.53%, 2.17% and 1.08%, respectively. Moreover, the errors of deep learning Markov model in stock price prediction of Shanghai Pudong Development Bank (sh600000), Guizhou Moutai (sh600519) and China Ping An Insurance (sh601318) are 2.56%, 2.98% and 3.56% respectively, which indicates that the four major financial industries in China have strong interdependence and risk contagion, so that the macro or systemic risks may arise, and the deep-learning Markov model can be adopted to predict the stock prices.

Methodology on Establishing Multivariate Failure Thresholds for Improved Remaining Useful Life Prediction in PHM

Prognostics and Health Management (PHM) methodologies and techniques have been much widely studied in the academia and practiced by the industry in recent years. Prognostic approaches commonly try to establish the relationship between Remaining Useful Life (RUL) and a single variable or health indicator (HI) which can be obtained from multi-sensor fusion or data-driven models. However, simply relying on a single variable could reduce RUL prediction robustness when it is less representative of the system health conditions. Taking multiple variables into consideration for RUL prediction, quantifying operating risks and determining multivariate failure threshold is essential yet rarely studied. Generally, there are three major challenges that limit the practicality of this topic. 1) How to determine the multivariate failure threshold? 2) How to quantify operation risks based on multiple variables? 3) How to make reliable extrapolations of future conditions? To address these questions, this paper proposes 1) a novel copula model to determine multivariate failure threshold, and 2) a Maximum Likelihood Estimation enhanced similarity-based Particle Filter (MLE-SMPF) to predict future system conditions. In the proposed methodology, the health assessment is firstly performed to obtain HI trajectory. The copula risk quantification model is then trained by two variables HI and life. The proposed copula model can easily include multiple variables compared with our previously published approach using bivariate Weibull Distribution[1]. Afterward, MLE-SMPF is used to extrapolate future HI for testing data. The prediction capability is further improved compared with [2] by introducing MLE for Particle Filter transition function parameter initialization. Finally, the system RUL is determined from the failure threshold which is obtained according to the quantified operation risk. The proposed methodology is validated on the C-MAPSS data from the PHM data competition 2008 hosted by PHM society. The result outperforms most of the benchmarks from recent publications. The proposed methodology is easy to transfer to other potential machine prognostic applications.

Copula in Wildfire Analysis: A Systematic Literature Review

Copula model is a method that can be implemented in various study fields, including analyzing wildfires. The copula distribution function gives a simple way to define joint distribution between two or more random variables. This study aims to review the application of copula in the analysis of wildfires using a Systematic Literature Review (SLR) and provide insight into research opportunities related to the application in Indonesia. The results show there are very few articles using the copula model in the analysis of wildfires. However, the increasing number of article citations each year shows the importance of such article research and has contributed to wildfire analysis development. In that article, 50% of studies applied the copula model to direct wildfire analysis (using fire data) in Canada, Portugal, and the US. Meanwhile, the other 50% use the copula model for indirect wildfire analysis (not using fire data) in Canada and the European region. The outcome of the presented review will provide the latest research positions and future research opportunities on the application of copula in the analysis of wildfires in Indonesia.Keywords: copula; wildfire; systematic literature review. AbstrakModel copula merupakan metode yang dapat diimplementasikan pada berbagai bidang penelitian, salah satunya pada analisis kebakaran hutan. Fungsi sebaran copula memberikan cara yang mudah untuk mendefinisikan sebaran peluang bersama antara dua peubah acak atau lebih. Tujuan penelitian ini mengulas penerapan model copula tersebut pada analisis kebakaran hutan dalam studi literatur menggunakan Systematic Literature Review (SLR) serta memberikan peluang riset ke depan terkait implementasinya pada analisis kebakaran hutan di Indonesia. Hasil penelitian menunjukkan bahwa model copula pada analisis kebakaran hutan masih sangat sedikit. Namun, peningkatan jumlah sitasi artikel tiap tahun menunjukkan pentingnya penelitian tersebut dan memiliki kontribusi pada perkembangan analisis kebakaran hutan. Pada artikel tersebut, sebanyak 50% penelitian menerapkan model copula pada analisis kebakaran secara langsung (menggunakan data kebakaran) di Kanada, Portugal, dan Amerika. Sementara, sebanyak 50% lainnya menerapkan model copula pada analisis kebakaran secara tak langsung (tidak menggunakan data kebakaran), yaitu di Kanada dan kawasan Eropa. Hasil tinjauan memberikan posisi riset terkini serta usulan riset ke depan mengenai penerapan model copula untuk analisis kebakaran hutan dan lahan di Indonesia.Kata kunci: copula; kebakaran hutan; studi literatur sistematik.

A Bayesian Copula Approach for Flood Analysis

This study aims to provide joint modelling of rainfall characteristics in Peninsular Malaysia using two-dimensional copula. Two commonly regarded as important variables in the field of hydrology, namely rainfall severity and duration were derived using the Standard Precipitation Index (SPI) and their univariate marginal distributions are further identified by fitting into several distributions. The paper uses a Bayesian framework to estimate the parameter values in the marginal and copula model. The approximation of the posterior distribution by random sampling has been done by Monte Carlo Markov Chain (MCMC). Next, the authors compared these findings with those based on the classical procedure. The results indicated that the Bayesian approach can be substantially more reliable in parameter estimation for small samples.

Research on the Dependence Structure and Risk Spillover of Internet Money Funds Based on C-Vine Copula and Time-Varying t-Copula

Internet money funds (IMFs) are the most widely involved products in the Internet financial products market. This research utilized the C-vine copula model to study the risk dependence structure of IMFs and then introduces the time-varying t-copula model to analyze the risk spillover of diverse IMFs. The results show the following: (1) The risks of Internet-based IMFs, bank-based IMFs, and fund-based IMFs have obvious dependence structure, and the degree of risk dependence among different categories of IMFs is significantly different. (2) There are risk spillover effects among diverse IMFs, and their risk dependence relationship is characterized by cyclical feature. (3) The risk spillover effect among diverse IMFs is pronounced, and dynamic risk dependence between IMFs is characterized by synchronization.