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Final Report Summary - ANLSDA (Advance Challenging Statistical Analysis for Massive High-Dimensional Nonlinear Spatial Time Series)

In general, nonlinear features in spatial/temporal modelling are not possible within the traditional scope of covariance structures, and require more sophisticated tools. This project under the support by the MC-CIG therefore aimed to explore and develop new tools for modelling and prediction with nonlinear time-lagged spatial neighbouring effects well considered for spatial time series data. In order to avoid the dangers of possible model mis-specification in using parametric approaches, we are developing nonparametric and semiparametric techniques for nonlinear spatio-temporal modelling and prediction, which allow the data to speak for themselves in determining the complex form of mathematical relationships between variables without prespecifying a parametric structure on the data-generating process.

Over the past four years, the work carried out to achieve the project's objectives includes: (i) We were developing nonparametric and semiparametric techniques for nonlinear spatial and time series modelling and prediction. These tools allow the data to speak for themselves in determining the complex form of mathematical relationships between spatial neighbouring time-lagged variables without prespecifying a possibly biased parametric structure on the data-generating process. (ii) Semiparametric spatial weighting scheme is fully developed with the idea of using spatial weights, specified by the modellers or experts with prior physical or economic information on the distance between sites. This scheme is popular in spatial econometrics. (iii) Semiparametric data-driven weighting scheme and possible underlying common factors have been basically well developed in our setting of spatial neighbouring time-lagged interactions. Some data-driven weighting methods were explored by combining semiparametric structures with the use of penalty functions such as adaptive Lasso. Such ideas are increasingly popular in the current literature on high-dimensional data, allowing us to estimate the time-lagged spatial neighbouring weights and select the most important common underlying neighbouring variables both in time and space in nonlinear prediction. (iv) Quantile regression analysis and risk modelling in applications. For example, semiparametric quantile methods are developed for spatial and time series data, and applications to the risk modelling and integrations of energy markets such as the USA’s state-level natural gas markets and the EU’s states’ gasoline markets, etc., are investigated.

We have fully tried to fulfil the overall objectives of the project with the main results and conclusions as well as their potential impact and use and socio-economic impact detailed as follows:

(i) This career integration grant has significantly helped the fellow to achieve important scientific progress and results, with 9 papers so far published or accepted under acknowledgement of funding support of this grant by such top journals as Journal of American Statistical Association and Journal of Econometrics, as well as Journal of Time Series Analysis and Scandinavian Actuarial Journal, etc.. In addition, over the project period (May 2014 – April 2018), there are 6 other publications and other working papers related to this project. These publications focus on new semiparametric methods developed for non-Gaussian/nonlinear modelling of spatial and time series data.

(ii) Not only so, this grant has greatly supported the fellow to develop his smooth transition in research from Australia to the UK as a professor/chair in statistics at University of Southampton, with a study group of RiSMOR (Research in Statistical Modelling and Optimisation on Risks) initiatively established by the fellow together with his colleagues for his research career development integrated with the colleagues at Southampton. This group has received increasing attention within University of Southampton and we are developing it into RISMOR (Research in Intelligent Statistical Modelling and Optimisation on Risks) in view of the challenges with big spatio-temporal data analysis and potential outperformance of intelligent modelling.

(iii) Moreover, four PhD students are being supervised by the fellow under the support of this grant, whose PhD programmes are associated with this project. These programmes include spatial flooding modelling, spatial temporal quantile regression analysis, spatial temporal energy network analysis of the EU and the USA energy market data, and spatial prediction of air quality data, etc. Therefore this CIG project has helped to get new generation researchers trained for future and will generate potential impacts in the related research and social-economic areas.

(iv) In addition, under the support of this grant, since May 2014, the fellow has actively participated in more than 20 local and international seminars, workshops and conferences, either as an invited speaker or as an organiser of the sessions of conferences, for examples, the fellow being the member of the Scientific Program Committee of the International Conferences on Computational and Financial Econometrics and/or organiser of sessions on spatial econometrics and financial time series econometrics over 2014-2018, which all greatly help promote the research and generate impact under this project with the objectives and impacts from this project more widely achieved.

(v) In order to illustrate and promote the work of the project, a particular project website was established for this project and has been being updated, the address of which can be linked at

In short, the work and results the fellow has established in the past four years have laid a solid base for the research on nonlinear spatial time series data analysis to continue to be developed following the current achievements, in particular towards intelligent nonlinear spatial-temporal modelling. It can be expected that the research the fellow will carry on based on the success of this project will continue to generate high quality publications and the active involvement in international academic activities in seminars, workshops and conferences, etc.. Therefore this project will continue to generate impact in research and potential socio-economic impact in future with more efficient, robust and intelligent methodologies to be pursued for practitioners and policy-makers.

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