By Christopher F. Baum
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Extra info for A review of Stata 8.1 and its time series
Xn are independent, identical copies of X. The only possible choice for cn is cn = n1/α . X is strictly stable if and only if dn = 0 for all n. Both, our definition of stable and the result above use distributional properties of X. While useful, this does not give a concrete way of parameterizing stable distributions. 28) α = 1. The exact form of the characteristic function chosen here is to guarantee certain statistically useful properties. The key idea is that α and β determine the shape of the distribution while A is a scale and B is a shift.
Org. org, with its Annual Report, the World Economic Outlook, and the International Capital Markets Report. Especially, many of the tables and graphs presented in the text were copied from these sources. For the historical development of financial markets I borrowed from two books: The description of the market movers was taken from the book Market Movers by Dunnan and Pack (1993), and the material on investment environments in finance was taken from the book International Portfolio Management - A Modern Approach written by Watsham (1993).
Note, that tan(πα/2) = 0, so the characteristic function is real and hence the distribution is always symmetric, no matter what the value of β. Parameterization A general stable distribution requires four parameters to describe: the stable index α, the skewness β and a scale and a shift parameter. It is an historical fact that several different parameterizations are used for stable distributions. We will use γ for the scale parameter and δ for the location parameter, so that the four parameters will be (α, β, γ, δ).