PHD ORAL PRESENTATION
Modern big data contain rich information that can be used to improve the understanding and predictability of real problem. However, the common features of the data with high dimensionality (HD) and high frequency (HF) bring theoretical and numerical challenges in modeling and estimation. In this thesis, three statistical methods are proposed to model the dynamic dependence of the HD and HF data. First, day-ahead natural gas flows are forecasted using a Functional Autoregressive with eXogenous variable (FARX) approach. It not only models the functional curves of gas flow, but also takes into consideration of the contributions of functional exogenous variables. Next, the joint dynamics of the liquidity demand and supply in the Limit Order Book (LOB) are modelled using a unified Vector Functional AutoRegressive (VFAR) framework. It is flexible to model multiple functional curves simultaneously. Lastly, a Markov Switching (MS) regression model is proposed to estimate resilience from LOB records. The MS regime improves model estimation by allowing time-varying coefficients, which takes into consideration of the instability of the time series.