Surface time series models for large spatio-temporal datasets

Abstract

The data observed in many phenomena have a spatial and a temporal component. Due to the rapid development of complex, 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. Therefore, 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 obtain 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.