Estimation of spatio-temporal extreme distribution using a quantile factor model

This paper describes the estimation of the extreme spatio-temporal sea surface temperature data based on the quantile factor model implemented by the SNU multiscale team. The proposed method was developed for the EVA2019 Data Challenge. Various attempts have been conducted to use factor models in spatio-temporal data analysis to find hidden factors in high-dimensional data. Factor models represent high-dimensional data as a linear combination of several factors, and hence, can describe spatially and temporally correlated data in a simple form. Meanwhile, unlike ordinary factor models, there are asymmetric norm-based factor models, such as quantile factor models or expectile dynamic semiparametric factor models, that can help understand the quantitative behavior of data beyond their mean structure. For this purpose, we apply a quantile factor model to the data to obtain significant factors explaining the quantile response of the temperatures and find quantile estimates. We develop a new method for inference of quantiles of extremal levels by extrapolating quantile estimates from the factor model with extreme value theory. The proposed method provides better performance than the benchmark, gives some interpretable insights, and shows the potential to expand the factor model with various data.