Analysis of Financial Time Series, Third Edition

1.3 Processes Considered

Besides the return series, we also consider the volatility process and the behavior of extreme returns of an asset. The volatility process is concerned with the evolution of conditional variance of the return over time. This is a topic of interest because, as shown in Figures 1.2 and 1.3, the variabilities of returns vary over time and appear in clusters. In application, volatility plays an important role in pricing options and risk management. By extremes of a return series, we mean the large positive or negative returns. Table 1.2 shows that the minimum and maximum of a return series can be substantial. The negative extreme returns are important in risk management, whereas positive extreme returns are critical to holding a short position. We study properties and applications of extreme returns, such as the frequency of occurrence, the size of an extreme, and the impacts of economic variables on the extremes, in Chapter 7.

Other financial time series considered in the book include interest rates, exchange rates, bond yields, and quarterly earning per share of a company. Figure 1.5 shows the time plots of two U.S. monthly interest rates. They are the 10-year and 1-year Treasury constant maturity rates from April 1954 to February 2009. As expected, the two interest rates moved in unison, but the 1-year rates appear to be more volatile. Figure 1.6 shows the daily exchange rate between the U.S. dollar and the Japanese yen from January 4, 2000, to March 27, ...