An Online Sequential Learning Non-parametric Value-at-Risk Model for High-Dimensional Time Series

Online Value-at-Risk (VaR) analysis in high-dimensional space remains a challenge in the era of big data. In this paper, we propose an online sequential learning non-parametric VaR model called OS-GELM which is an autonomous cognitive system. This model uses a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process and an online sequential extreme learning machine (OS-ELM) to cognitively calculate VaR, which can be used for online risk analysis. The proposed model not only learns the data one-by-one or chunk-by-chunk but also calculates VaR in real time by extending OS-ELM from machine learning to the non-parametric GARCH process. The GARCH process is also extended to one-by-one and chunk-by-chunk mode. In OS-GELM, the parameters of hidden nodes are randomly selected. The output weights are analytically determined based on the sequentially arriving data. In addition, the generalization performance of the OS-GELM model attains a small training error and generates the smallest norm of weights. Experimentally obtained VaRs are compared with those given by GARCH-type models and conventional OS-ELM. The computational results demonstrate that the OS-GELM model obtains more accurate results and is better at forecasting the online VaR. OS-GELM model is an autonomous cognitive system to dynamically calculate Value-at-Risk, which can be used for online financial risk assessment about human being's behavior. The OS-GELM model can calculate VaR in real time, which can be used as a tool for online risk management. OS-GELM can handle any bounded, non-constant, piecewise-continuous membership function to realize real-time VaR monitoring.