DNA, Words and Models, Statistics of Exceptional Words

the intended audience. Several of the topics (such as martingales, stochastic differential equations, and multivariate time series) are rather advanced. The authors have both contributed associated S+ software, much of which is available as an add-on (for purchase) module (S+FinMetrics). The book covers some aspects of financial time series, associated analysis challenges, and S+ software. I would prefer that some of the financial time series descriptions were collected in a convenient location, say in one chapter. Instead, various time series concepts are introduced in many chapters, organized somewhat according to the recommended analysis technique(s). The index omits many of the covered topics, so this forced me to thumb through the many pages several times when searching various topics. There is enough S+ detail to increase one’s S+ skills, although there is only a very brief attempt in Chapter 1 to provide systematic S+ instruction, essentially on an as-needed basis for understanding how to use S+FinMetrics. I like the style (one example is on p. 2) of showing an example of S+ coding that does not work, along with effective but brief explanation. The 23 chapters and 900 pages are too dense to list and summarize here. Instead I will list a few things I like and do not like about the book. I like the reference style with well-written concise explanations. For example, I was not aware of a generalization to the Fisher–Tippet result that extends results for extreme values from the independent and identically distributed case to the stationary case; this is one of many practical examples (what is the distribution for my maximum gain or loss in a certain investment over time) that cites rigorous statistical literature. I also like the 1-page discussion of the logic behind an “investment’s β . ” Writing the “famous” capital asset pricing model (CAPM) as Rit − rft = αi + βi(RMt − rft) + εit , i = 1, . ,N; t = 1, . ,T , will not intimidate a statistician although most statisticians will need help with the financial logic. How many of us have seen a clear description of the CAPM in a typical investment firm’s glossy newsletter? Here, Rit is the return on asset i between time periods t − 1 and t,RMt is the return on a relevant market index (that the asset i is being compared to), rft is the rate of return on a risk-free asset between time periods t − 1 and t and εit ∼ GWN(0, σ 2), which is the text’s notation for Gaussian white noise. Perhaps readers of this review will appreciate seeing the CAPM and can interpret it without the help provided in the text. This is one of the simplest financial examples in the text, so be aware that the mathematical and statistical subjects covered are (to me) rather advanced. The well-written reference style avoids technical details however. I also mention the CAPM here because I am reminded of Dr. Fred Leyseiffer’s comment to me when I was a first-year graduate student in the Florida State University statistics department. “They never care about money. ” This referred to PhD students who chained themselves to their office desk for 14 hours per day. Well, I now care about money to the extent that I wanted to know how to interpret a “fund’s β” so the text is useful for that rather trivial reason alone. Another good aspect of this text is its surprisingly wide and reasonably deep coverage of a lot of practical and theoretical time series concepts. To be balanced, I must mention a few suggested improvements. First, I could not get a sense when real progress had been made with financial time series forecasting using relatively new approaches such as GARCH (generalized autoregressive conditional heteroskedasticity) models. GARCH dates to 1981 and today is often cited, and I have no doubt that GARCH models fit many time series better than standard ARMA (autoregressive moving average) models. Maybe that justifies their popularity, but perhaps a revision could show or at least cite practical comparisons among forecasts from competing models when applied to real data (there are many real data examples but I did not find any performance comparisons among methods). The GARCH case is but one such example where there is not a practical demonstration of a performance advantage that might matter in a financial sense using real data. To rephrase this small suggestion, could a revision include examples where a basic, naive approach is outperformed in a practical sense by one of the available advanced methods? There are many examples where models were extended to capture various features of the data, such as GARCH. And, note that the S+FinMetrics module provides GARCH model simulation and selection features, among much other S+ functionality for rather advance methods. Second, there are some occasional loose descriptions. For example, on page 68 in describing the shape of the autocorrelation plot (ACF) from lags 1 to 25, the text indicates that the slowly varying ACF values indicate “persistence,” but leaves the reader hanging and never returns to this example interest rate differential data having persistent ACF values. Chapter 8 involves long memory time series where persistence is given a definition, so a reread of page 68 after reading Chapter 8 is suggested. There is also lack of an adequate discussion of why and to what extent the partial ACF is more effective than the ACF for choosing an AR order for such data. In short, the text is not recommended for learning ARMA or other time series concepts, although it would be a fantastic complement to traditional texts that are often used to teach time series (Chatfield 1980). Third, I note that S+FinMetrics does not offer an ARMA-based disaggregation function. Disaggregation is discussed (pp. 35–38), but the function options do not include concepts such as those in (Al-Osh 1989). It could be that the basic function options that are provided are nearly as effective and much simpler to understand and implement. Overall, it is a pleasure to strongly recommend this text, and to include statisticians such as myself among the pleased audience. The statistical technical detail is approximately on the level of (Venables and Ripley 1999). I think the financial subject matter is at an appropriate level, and is perhaps written more for the intended statistical audience than for financial students. Finally, I note that the first author’s website invites suggested improvements; errors are being collected presumably to improve a third edition. Datasets and S+FinMetrics are available through Insightful.