Abstract
This book is about the statistical analysis of financial markets data such as equity prices, foreign exchange rates, and interest rates. These quantities vary randomly thereby causing financial risk as well as the opportunity for profit. Figures 4.1, 4.2, and 4.3 show, respectively, time series plots of daily log returns on the S&P 500 index, daily changes in the Deutsch Mark (DM) to U.S. dollar exchange rate, and changes in the monthly risk-free return, which is 1/12th the annual risk-free interest rate. A time series is a sequence of observations of some quantity or quantities, e.g., equity prices, taken over time, and a time series plot is a plot of a time series in chronological order. Figure 4.1 was produced by the following code:
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Notes
- 1.
See Appendix A.2.1 for definitions of CDF, PDF, and other terms in probability theory.
- 2.
“Standard” means having expectation 0 and variance 1.
- 3.
See Sect. 5.16 for more discussion of robust estimation and the precise definition of MAD.
- 4.
Somewhat confusingly, the bottom 10 % of the data is also called the first decile and similarly for the second 10 %, and so forth. Thus, the first decile could refer to the 10th percentile of the data or to all of the data at or below this percentile. In like fashion, the bottom 20 % of the sample is called the first quintile and the second to fifth quantiles are defined analogously.
- 5.
See Appendix A.9.4 for an introduction to the lognormal distribution and the definition of the log-standard deviation.
- 6.
However, t-distributions have been generalized in at least two different ways to the so-called skewed-t-distributions, which need not be symmetric. See Sect. 5.7
- 7.
See Sect. 5.14
- 8.
See Chap. 19 for a discussion on how tail weight can greatly affect risk measures such as VaR and expected shortfall.
- 9.
The factor 1.5 is the default value of the range parameter and can be changed.
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Ruppert, D., Matteson, D.S. (2015). Exploratory Data Analysis. In: Statistics and Data Analysis for Financial Engineering. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2614-5_4
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