"Frontmatter". In: Analysis of Financial Time Series

PROCESSES CONSIDERED 17density0.0 0.02 0.04 0.06 0.08density0.0 0.02 0.04 0.06 0.08-20 0 20 40s-rtn-20 0 20l-rtnFigure 1.4. Comparison of empirical and normal densities for the monthly simple and logreturns of IBM stock. The sample period is from January 1926 to December 1997. The leftplot is for simple returns and the right plot for log returns. The normal density, shown by thedashed line, uses the sample mean and standard deviation given in Table 1.2.returns. (f) The descriptive statistics show that the difference between simple and logreturns is not substantial.Figure 1.4 shows the empirical density functions of monthly simple and logreturns of IBM stock. Also shown, by a dashed line, in each graph is the normalprobability density function evaluated by using the sample mean and standarddeviation of IBM returns given in Table 1.2. The plots indicate that the normalityassumption is questionable for monthly IBM stock returns. The empirical densityfunction has a higher peak around its mean, but fatter tails than that of the correspondingnormal distribution. In other words, the empirical density function is taller,skinnier, but with a wider support than the corresponding normal density.1.3 PROCESSES CONSIDEREDBesides the return series, we also consider the volatility process and the behavior ofextreme returns of an asset. The volatility process is concerned with the evolution ofconditional variance of the return over time. This is a topic of interest because, asshown in Figures 1.2 and 1.3, the variabilities of returns vary over time and appear in