Forecasting Tail Risk of Time Series with Weighted Scoring Rules

In resource management or financial field, extreme events such as downpour, drought or bankruptcy are main research topics since they may incur severe problems. Many studies have built on tails in distribution of resource and return to forecast future events for a provision plan. This study especially focuses on tail risk such as Value-at-Risk(VaR) in time series to predict resource exhaustion. Using weighted continuous ranked probability score(CRPS) as loss function we impose larger weights to lower quantiles. To tackle intractable integral in loss function we exploit monotonic linear splines which parameterize the qunatile function and it gives rise to closed form of the integral. In our methods, deep learning models like transformers return the parameters of monotonic linear spline that allow for quantile estimation. In numerical studies, we compare probabilistic forecasters and their property in lower quantile estimation with real-world time series datasets.