Surface time series models for large spatio-temporal datasets

The data observed in many phenomena have a spatial and a temporal component. Due to the rapid development of com-plex, performant technologies, spatio-temporal data can now be collected on a large scale. However, the statistical modeling of large sets of spatio-temporal data involves several challenging problems. For example, it is computationally challenging to deal with large datasets and spatio-temporal nonstationarity. There-fore, the development of novel statistical models is necessary. Here, we present a new methodology to model complex and large spatio-temporal datasets. In our approach, we estimate a continuous surface at each time point, and this captures the spatial dependence, possibly nonstationary. In this way, the spatio-temporal data result in a sequence of surfaces. Then, we model this sequence of surfaces using functional time series techniques. The functional time series approach allows us to ob-tain a computationally feasible methodology, and also provides extensive flexibility in terms of time-forecasting. We illustrate these advantages through a Monte Carlo simulation study. We also test the performance of our method using a high-resolution wind speed simulated dataset of over 4 million values. Overall, our method uses a new paradigm of data analysis in which the random fields are considered as a single entity, a very valuable approach in the context of big data. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

The development of complex and performant technologies enables the collection of large-scale spatio-temporal data. However, statistically modeling such datasets poses various challenges, including dealing with large datasets and nonstationarity. This research proposes a novel methodology that estimates continuous surfaces at each time point and models the sequence of surfaces using functional time series techniques. The advantages of this approach are demonstrated through a simulation study and the analysis of a high-resolution wind speed dataset. Overall, this method offers a valuable approach in the context of big data by considering random fields as a single entity.