Summary

In this chapter, we focused on several issues, especially on volatility measures and ARCH/GARCH. For the volatility measures, first we discussed the widely used standard deviation, which is based on the normality assumption. To show that such an assumption might not hold, we introduced several normality tests, such as the Shapiro-Wilk test and the Anderson-Darling test. To show a fat tail of many stocks' real distribution benchmarked on a normal distribution, we vividly used various graphs to illustrate it. To show that the volatility might not be constant, we presented the test to compare the variance over two periods. Then, we showed a Python program to conduct the Breusch-Pangan (1979) test for heteroskedasticity. ARCH and GARCH are used widely to describe the evolution of volatility over time. For these models, we simulate their simple form such as ARCH (1) and GARCH (1,1) processes. In addition to their graphical presentations, the Python codes of Kevin Sheppard are included...