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Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery. (English) Zbl 1326.91035
Summary: Low-frequency financial returns can be modelled as centered around piecewise-constant trend functions which change at certain points in time. We propose a new stochastic time series framework which captures this feature. The main ingredient of our model is a hierarchically-ordered oscillatory basis of simple piecewise-constant functions. It differs from the Fourier-like bases traditionally used in time series analysis in that it is determined by change-points, and hence needs to be estimated from the data before it can be used. The resulting model enables easy simulation and provides interpretable decomposition of nonstationarity into short- and long-term components. The model permits consistent estimation of the multiscale change-point-induced basis via binary segmentation, which results in a variablespan moving-average estimator of the current trend, and allows for short-term forecasting of the average return.

91G70 Statistical methods; risk measures
91B84 Economic time series analysis
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M07 Non-Markovian processes: hypothesis testing
R; basta
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