In Chapter 1, we give a brief introduction to univariate extreme value theory. We also discuss the kernel method of density estimation and non-parametric regression analysis. Some methods of window-width choosing are also given. In Chapter 2, we develop a differentiable kernel estimator for the dependence function of a bivariate extreme value distribution. The estimator is applied to different sets of bivariate extreme value data. In Chapter 3, some existing methods for testing bivariate extreme pairs are discussed. Two new methods of testing independence against the alternative of a general bivariate extreme value distribution are given. Chapter 4 is concerned with the extension of our kernel estimator to higher dimensional cases. The estimator is applied to a set of bivariate data. In Chapter 5, we look into some non-linear and non-Gaussian time series models. Based on the bivariate extreme value distribution, we propose a new time series model with first order Markov property. The model is applied to a sequence of wave height data.