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This book presents a new statistical method of constructing a price
index of a financial asset where the price distributions are skewed
and heavy-tailed and investigates the effectiveness of the method.
In order to fully reflect the movements of prices or returns on a
financial asset, the index should reflect their distributions.
However, they are often heavy-tailed and possibly skewed, and
identifying them directly is not easy. This book first develops an
index construction method depending on the price distributions, by
using nonstationary time series analysis. Firstly, the long-term
trend of the distributions of the optimal Box-Cox transformed
prices is estimated by fitting a trend model with time-varying
observation noises. By applying state space modeling, the
estimation is performed and missing observations are automatically
interpolated. Finally, the index is defined by taking the inverse
Box-Cox transformation of the optimal long-term trend. This book
applies the method to various financial data. For example, applying
it to the sovereign credit default swap market where the number of
observations varies over time due to the immaturity, the spillover
effects of the financial crisis are detected by using the power
contribution analysis measuring the information flows between
indices. The investigations show that applying this method to the
markets with insufficient information such as fast-growing or
immature markets can be effective.
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