HIGH-DIMENSIONAL TIME SERIES MODELLING AND FORECASTING WITH APPLICATION TO HIGH-FREQUENCY FINANCIAL AND ENERGY DATA

Abstract

Modern big data contain rich information that can be used to improve the understanding and predictability of real problem. However, the high dimensionality and high frequency features bring theoretical and numerical challenges in modeling and estimation. In this thesis, three statistical methods are proposed to model the dynamic dependence of these data. First, day-ahead natural gas flows are forecasted using a Functional AutoRegressive with eXogenous variable (FARX) approach. It models functional curves of gas flow together with the contribution of functional exogenous variables. Next, joint dynamics of 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, 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 the instability of the time series into consideration.