Statistical Modelling of Extreme Rainfall in Taiwan

In this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model. The non-stationary model means that the parameter of location of the GEV distribution is formulated as linear and quadratic functions of time to detect temporal trends in the maximum rainfall. Future behavior refers to the return level and the return period of the extreme rainfall. The 10, 20, 50 and 100-years return levels and their 95% confidence intervals of the return levels stationary models are provided. The return period is calculated based on the record-high (ranked 1st) extreme rainfall brought by the top 10 typhoons for each station in Taiwan. The estimates show that non-stationary model with increasing trend is suitable for the Kaohsiung, Hengchun, Taitung and Dawu stations. The Kaohsing and Hengchun stations have greater trends than the other two stations, showing that the positive trend extreme rainfall in the southern region is greater than in the eastern region of Taiwan. In addition, the Keelung, Anbu, Zhuzihu, Tamsui, Yilan, Taipei, Hsinchu, Taichung, Alishan, Yushan and Tainan stations are fitted well with the Gumbel distribution, while the Sun Moon Lake, Hualien and Chenggong stations are fitted well with the GEV distributio

Value at Risk models with long memory features and their economic performance

We study alternative dynamics for Value at Risk (VaR) that incorporate a slow moving component and information on recent aggregate returns in established quantile (auto) regression models. These models are compared on their economic performance, and also on metrics of first-order importance such as violation ratios. By better economic performance, we mean that changes in the VaR forecasts should have a lower variance to reduce transaction costs and should lead to lower exceedance sizes without raising the average level of the VaR. We find that, in combination with a targeted estimation strategy, our proposed models lead to improved performance in both statistical and economic terms