Statistics and Its Interface

Volume 6 (2013)

Number 4

Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery

Pages: 449 – 461



Piotr Fryzlewicz (Department of Statistics, London School of Economics, London, United Kingdom)

Anna Louise Schröder (Department of Statistics, London School of Economics, London, United Kingdom)


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.


financial time series, adaptive trend estimation, change-point detection, binary segmentation, unbalanced Haar wavelets, frequency-domain modelling

Published 10 January 2014