Abstract
Nonstationary financial time series often observed in the real world, include a time series with a slowly shifting mean value function, a time series with time-varying variations around the mean value, and a time series with both a moving mean value and changing waveforms around the mean value. First, we briefly review nonstationary time series modeling, such as trend estimation, time-varying variance modeling, seasonal adjustment modeling, and non-Gaussian distribution modeling, which is closely related to our method for constructing a distribution-free index. Since the distribution of prices of a financial market is often non-Gaussian, we propose to transform the price observations by the Box–Cox transformation. Then, a 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 to the Box–Cox transformed observations. The new index becomes impartial, regardless of the price distributions.
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Tanokura, Y., Kitagawa, G. (2015). Method for Constructing a Distribution-Free Index. In: Indexation and Causation of Financial Markets. SpringerBriefs in Statistics(). Springer, Tokyo. https://doi.org/10.1007/978-4-431-55276-5_2
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DOI: https://doi.org/10.1007/978-4-431-55276-5_2
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