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

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  • Schröder, Anna Louise
  • Fryzlewicz, Piotr

Abstract

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 variable-span moving-average estimator of the current trend, and allows for short-term forecasting of the average return.

Suggested Citation

  • Schröder, Anna Louise & Fryzlewicz, Piotr, 2013. "Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery," MPRA Paper 52379, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:52379
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    File URL: https://mpra.ub.uni-muenchen.de/52379/1/MPRA_paper_52379.pdf
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    1. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value-at-Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    2. Hernando Ombao & Jonathan Raz & Rainer von Sachs & Wensheng Guo, 2002. "The SLEX Model of a Non-Stationary Random Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 171-200, March.
    3. Cizek, P. & Haerdle, W. & Spokoiny, V., 2007. "Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models," Discussion Paper 2007-35, Tilburg University, Center for Economic Research.
    4. Fryzlewicz, Piotr, 2007. "Unbalanced Haar Technique for Nonparametric Function Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1318-1327, December.
    5. Hasabrouck, Joel & Sofianos, George, 1993. " The Trades of Market Makers: An Empirical Analysis of NYSE Specialists," Journal of Finance, American Finance Association, vol. 48(5), pages 1565-1593, December.
    6. G. P. Nason & R. von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    7. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(03), pages 315-352, June.
    8. Piotr Fryzlewicz & Theofanis Sapatinas & Suhasini Subba Rao, 2006. "A Haar--Fisz technique for locally stationary volatility estimation," Biometrika, Biometrika Trust, vol. 93(3), pages 687-704, September.
    9. P. Čížek & W. Härdle & V. Spokoiny, 2009. "Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 248-271, July.
    10. Gençay, Ramazan & Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon J., 2001. "An Introduction to Wavelets and Other Filtering Methods in Finance and Economics," Elsevier Monographs, Elsevier, edition 1, number 9780122796708.
    11. Pan, Jianmin & Chen, Jiahua, 2006. "Application of modified information criterion to multiple change point problems," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2221-2241, November.
    12. Lee, Chung-Bow, 1995. "Estimating the number of change points in a sequence of independent normal random variables," Statistics & Probability Letters, Elsevier, vol. 25(3), pages 241-248, November.
    13. Leitch, Gordon & Tanner, J Ernest, 1991. "Economic Forecast Evaluation: Profits versus the Conventional Error Measures," American Economic Review, American Economic Association, vol. 81(3), pages 580-590, June.
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    Keywords

    Financial time series; Adaptive trend estimation; Change-point detection; Binary segmentation; Unbalanced Haar wavelets; Frequency-domain modelling;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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