Statistics for tempo-spatial data is one of the most important research frontiers in modern statistics. This project proposes to introduce and develop the concept of tempo-spatial stochastic volatility, which allows one to model volatility clusters both in time and in space. Empirical evidence for stochastic volatility is ubiquitous, and hence, it is vital and urgent that statistical models and estimation methods will be developed to account for this key quantity.Stochastic volatility is a latent variable, meaning that it is not directly observable but needs to be estimated from other (observable) variables. The main research objectives are to construct novel, non-parametric estimators for tempo-spatial stochastic volatility and to establish the corresponding asymptotic theory for constructing confidence regions. Moreover, fully parametric classes of stochastic volatility models will be developed, and the corresponding statistical inference techniques will be derived.The objectives will be achieved by developing the concept of realised quadratic variation for random fields, which results in a non-parametric proxy for tempo-spatial stochastic volatility. Also, novel, parametric estimation procedures will be designed to estimate the parameters of new tempo-spatial stochastic volatility models based on a quasi-maximum-likelihood framework.The completion of this project will be a major breakthrough in statistics and will solidify Europe’s leadership in this field. Moreover, it is of key relevance to the Work Programme since it strongly contributes to the initiative “sustainable growth”: The results of this research project are directly applicable to, e.g. measuring and modelling the risk associated with climate change and to finding an optimal design for wind farms, making renewable sources of energy more efficient and reliable.