Nonlinear Spatio-temporal Modelling Theory with Application

Abstract

A large number of spatio-temporal data with sophisticated structures exist in all kinds of disciplines such as energy research, environmental sciences, urban economics, etc. Nonlinear modelling of such spatio-temporal data is often a challenge, with irregularly observed locations and location-wide non-stationarity (c.f., Lu et al., 2009; Al-Sulami et al., 2017a). This thesis sheds new light on both theoretical investigation into the spatio-temporal model with varying coefficient structure and empirical application to the complex dynamic nature of spatio-temporal data in energy market.
The main contributions of the thesis are as following:
(1) Chapter 2 empirically investigates the dynamic integrations or linkages of the USA's natural gas markets at the state level in a holistic manner by proposing a spatio-temporal network quantile analysis. This chapter empirically finds that spatial neighbouring effects significantly exist among the natural gas markets, not only in the eastern and middle states but also in some western and southwest states, and so do the dynamic linkages to the national crude oil market for the natural gas markets in the southern and eastern states, which are heterogeneous at different quantile levels. The empirical findings can help investors to hedge against the energy price risks in maximizing profits and local industry and government to mitigate the negative impacts from the expected or unexpected fluctuations in the national oil and the neighbouring natural gas markets.
(2) In Chapter 3, we are mainly concerned with the nonlinear modelling of econometric time series data from the view point of quantile regression. Specifically, we consider quantile regression for a (strictly) stationary time series that is near epoch dependent (NED). It is an extension of the work of Welsh (1996) and Yu and Jones (1998) under i:i:d: samples to econometric time series. Our asymptotic normality result generalizes Lu et al. (1998), Honda (2000) and Hallin et al. (2009a) who obtained Bahadur representations with different conditions under-mixing dependence to a more widely applicable family of data generating processes of near epoch dependence. It also lays the foundation for establishing asymptotic properties of nonlinear quantile modelling for spatio-temporal data under NED.
(3) In Chapter 4, we propose a semiparametric family of Dynamic Functional coefficient Autoregressive Spatio-Temporal (DyFAST) models to address the modelling and analysis of spatio-temporal data, Yt(si), t = 1; : : : ; T and i = 1; 2; ;N, featuring non-stationarity over irregular locations in space. It is a useful extension and combination of spatial autoregressive models (Ord, 1975; Gao et al., 2006; Kelejian and Prucha, 2010; Su and Jin, 2010) and varying coefficient models (Zhang and Fan, 1999; Wang and Xia, 2009; Zhang et al., 2009) as well as Al-Sulami et al. (2017a, 2019). To model the dynamic spatial neighbouring temporal lagged effects with the irregular locations, we consider using spatial weight matrix pre-specified either by experts or by the prior information of spatial locations, which is popular in spatial econometrics. Moreover, both one-step and two-step estimation methods are proposed to estimate the functional cofficients in DyFAST models. Accordingly, different semiparametric smoothing estimation procedures are suggested. Both theoretical properties and Monte Carlo simulations are investigated.
Our empirical applications to energy market data sets further illustrate the usefulness of the models.
(4) In Chapter 5, we propose a semiparametric spatio-temporal quantile model to further study the dynamic nature of non-normal spatio-temporal data. The quantile estimators are more robust than the mean estimators considered in Chapter 4 for non-normal spatio-temporal data. Moreover, this approach can provide more information about the dynamic spatial effects at different quantile levels. Both theoretical asymptotic properties and Monte Carlo simulations for our model are established.

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ORCID for Zudi Lu: orcid.org/0000-0003-0893-832X

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