This book presents a new practical method for constructing an index of prices of a financial asset for the case in which the distributions are skewed and heavy-tailed, using nonstationary non-Gaussian multivariate time series analysis. In order to facilitate the identification of the distribution, the observations are transformed by the Box-Cox transformation. A new distribution-free index is defined by taking the inverse Box-Cox transformation of the optimal long-term trend, which is estimated by fitting a trend model with time-varying observation noises. In order to detect causations between financial markets which are mostly entangled and may cause inextricable difficulties, such as financial crises, this book proposes the application of the generalized power contribution, which reveals the frequency-wise effect of multidimensional noise sources on the power of fluctuation of each variable in a multivariate feedback system. Applications to financial and economic time series data are used to investigate the effectiveness of the new index by power contribution analysis, and confirm that applying our indexation method to markets with insufficient information, such as fast-growing or immature markets, can be effective.
KeywordsHeavy-tailed Box-Cox transformation Trend model with time-varying observation noises Power contribution Distribution-free index
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