Weather Derivative Valuation: The Meteorological, Statistical, Financial and Mathematical Foundations

Read any paper in statistical meteorology or climatology since 1995 and you are nearly certain to find a citation of the first edition of this book (Wilks 1995). This is for good reason. The book is an excellent and complete introduction to applied statistics in the atmospheric sciences. The examples are all current, and the explanations of methods are transparently clear. The original has been used successfully as a textbook. The new edition contains many new topics, including density estimation, the bootstrap, and numerical methods in parameter fitting. Many of the examples are new, and there are several new problems at the end of each chapter. The most substantial additions come in the new Section 3, “Multivariate Statistics.” All of the standard topics are covered: a review of matrix algebra, multinomial distributions, principal components (called “empirical orthogonal functions” in meteorology), canonical correlation analysis, discrimination and classification, and cluster analysis. A regular, applied multivariate course could be (and has been) taught with this part of the book. Multidimensional statistics and massive datasets are meteorology nowadays, and this is the only book that presents a complete summary of the methods in common use. What makes this book specific to meteorology, and not just to applied statistics, are its extensive examples and two chapters on statistical forecasting and forecast evaluation. Most weather forecasts start as output from dynamical models, which are essentially enormous sets of partial differential equations and parameterizations that describe the physics of the atmosphere. The models are fed initial conditions, which are observations that go through a process called analysis that synchronizes the observations and model physics. Then the models are integrated forward in time. What comes out is a rough prediction of the future. Statistical models take these rough guesses and make them better. Naturally, there are many ways to do this, and many ways yet to be discovered. Wilks does a good job explaining what is known and what is not known. The newest twist in the forecast process, and one that recognizes the chaotic nature of the atmosphere, is called ensemble forecasting. The initial conditions are not without uncertainty, and so they are perturbed (in another complicated process of analysis) in such a way as to represent this uncertainty, and the dynamical models are rerun many times, each time with different perturbed initial conditions. The resulting ensemble of forecasts must be statistically postprocessed to produce (and display) a usable forecast. How to best do this is an open question, but again the book lays out the common strategies now in use. Once the forecasts (of any type) are in hand, they must be evaluated for accuracy using statistical methods. How to do this for point forecasts is now fairly well understood; the concepts of skill, proper probability forecasts, economic value, and graphical methods are all given here. But another big open question is how to do evaluation for multidimensional multivariate forecasts, a problem that few have yet tried to tackle, although some progress is being made. Actually, meteorologists have led the way in the statistical evaluation of predictions, and it would be wise for statisticians to take notice of these methods and begin to apply them routinely to their own models. For example, in how many applied papers in, say, sociology journals, can you recall that the model touted by the authors was actually verified and evaluated or just taken as finally proved (with an acceptably low p value)?