Multivariate Extreme Value Theory with an application to climate data in the Western Cape Province - Bhagwandin, Lipika (Department of Statistical Sciences, 2017)
An understanding of past and current weather conditions can aid in identifying trends and changes that have occurred in weather patterns. This is particularly important as certain weather conditions can have both a positive and a negative impact on various activities in any region. Together with an ever-changing climate it has become markedly noticeable that there is an upward trend in extreme weather conditions. The aim of this study is to evaluate the efficacy of univariate and multivariate extreme value theory models on climate data in the Western Cape province of South Africa. Data collected since 1965 from five weather stations viz. Cape Town International Airport, George Airport, Langebaanweg, Plettenberg Bay and Vredendal was modelled and analysed. In the multivariate analysis, multiple variables are modelled at a single location. Block maxima, threshold excess and point process approaches are used on the weather data, specifically on rainfall, wind speed and temperature maxima. For the block maxima approach, the data is grouped in n-length blocks and the maxima of each block form the dataset to be modelled. The threshold excess and point process approaches use a suitably chosen threshold whereby observations above the threshold are considered as extreme and therefore form the dataset used in the models. Under the threshold excess approach, only observations that exceed the threshold in all components are able to be modelled, whereas exceedances in one and all components simultaneously can be handled by the point process approach. While the probability of experiencing high levels of rainfall, wind speed and temperature individually and jointly are low, a few conclusions were drawn based on the comparison of the performance of the models. It was found that models under the block maxima approach did not perform well in modelling the weather variables at the five stations in both the univariate and multivariate case as many useful observations are discarded. The threshold excess and point process approaches performed better in modelling the weather extremes. Similar results are achieved between these two approaches in the univariate analysis and there is no outright distinction that favours one approach over the other. In terms of the multivariate case, which is restricted to two variables, the point process approach was able to provide estimates with increased accuracy as in many cases there are more extremes in one component individually than in both components. Specifically, the negative logistic and negative bilogistic models suitably capture the dependence structure between maximum wind speed versus maximum rain- fall and maximum wind speed versus maximum temperature at the five weather stations. The results from the point process models showed very weak dependence between wind speed and rainfall maxima as well as between wind speed and temperature maxima which may warrant the inclusion of additional variables into the analysis and even a spatial component which is not included in this study.