Schröder, Anna Louise and Fryzlewicz, Piotr (2013): Adaptive trend estimation in financial time series via multiscale changepointinduced basis recovery. Published in: Statistics and Its Interface , Vol. 4, No. 6 (2013): pp. 449461.

PDF
MPRA_paper_52379.pdf Download (1MB)  Preview 
Abstract
Lowfrequency financial returns can be modelled as centered around piecewiseconstant 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 hierarchicallyordered oscillatory basis of simple piecewiseconstant functions. It differs from the Fourierlike bases traditionally used in time series analysis in that it is determined by changepoints, 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 longterm components. The model permits consistent estimation of the multiscale changepointinduced basis via binary segmentation, which results in a variablespan movingaverage estimator of the current trend, and allows for shortterm forecasting of the average return.
Item Type:  MPRA Paper 

Original Title:  Adaptive trend estimation in financial time series via multiscale changepointinduced basis recovery 
English Title:  Adaptive trend estimation in financial time series via multiscale changepointinduced basis recovery 
Language:  English 
Keywords:  Financial time series, Adaptive trend estimation, Changepoint detection, Binary segmentation, Unbalanced Haar wavelets, Frequencydomain modelling 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C58  Financial Econometrics G  Financial Economics > G1  General Financial Markets > G17  Financial Forecasting and Simulation 
Item ID:  52379 
Depositing User:  Ms Anna Louise Schröder 
Date Deposited:  26. Dec 2013 21:21 
Last Modified:  26. Dec 2013 21:24 
References:  Baek, C. and Pipiras, V. (2009). Long range dependence, unbalanced Haar wavelet transformation and changes in local mean level. International Journal of Wavelets, Multiresolution and Information Processing 7 23–58 Bai, J. (1997). Estimating multiple breaks one at a time. Econometric Theory 13 315–352 Baron, M., Brogaard, J. and Kirilenko, A. (2012). The trading profits of high frequency traders. Technical Report, Foster School of Business, University of Washington Berkowitz, J. and O’Brien, J. (2002). How accurate are valueatrisk models at commercial banks? Journal of Finance 57 1093–1111 Boysen, L., Kempe, A., Liebscher, V., Munk, A. and Wittich, O. (2009). Consistencies and rates of convergence of jumppenalized least squares estimators. Annals of Statistics 37 157–183 Bruder, B., Dao, T. L., Richard, J. C. and Roncalli, T. (2008). Trend filtering methods for momentum strategies. Technical Report, Lyxor Asset Management. Catalao, J. P. S., Mariano, S. J. P. S., Mendes, V. M. F. and Ferreira, L. A. F. M. (2007). Shortterm electricity prices forecasting in a competitive market: A neural network approach. Electric Power Systems Research 77 1297–1304 Cho, H. and Fryzlewicz, P. (2012). Multiscale and multilevel technique for consistent segmentation of nonstationary time series. Statistica Sinica 22 207–229 Delouille, V., Franke, J. and von Sachs, R. (2001). Nonparametric stochastic regression with designadapted wavelets. Sankhya: The Indian Journal of Statistics Series A 63 328–366 Fryzlewicz, P. (2007). Unbalanced Haar technique for nonparametric function estimation. Journal of the American Statistical Association 102 1318–1327 Fryzlewicz, P. (2012). Wild Binary Segmentation for multiple changepoint detection. Preprint. Fryzlewicz, P., Sapatinas, T. and Rao, S. S. (2006). A HaarFisz technique for locally stationary volatility estimation. Biometrika 93 687–704 Fryzlewicz, P. and Subba Rao, S. (2013). BaSTA: Consistent multiscale multiple changepoint detection. Preprint Garcia, R. C., Contreras, J., van Akkeren, M. and Garcia, J. B. C. (2005). A GARCH forecasting model to predict dayahead electricity prices. IEEE Transactions on Power Systems 20 867–874 Gencay, R., Selcuk, F. and Whitcher, B. J. (2001). An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Academic Press Girardi, M. and Sweldens, W. (1997). A new class of unbalanced Haar wavelets that form an unconditional basis for Lp on general measure space. Journal of Fourier Analysis and Applications 7 457–474 Hasbrouck, J. and Sofianos, G. (1993). The trades of market makers: An empirical analysis of NYSE specialists. Journal of Finance 48 1565–1593 Katz, J. O. and McCormick, D. (2000). The Encyclopedia of Trading Strategies. McGrawHill, New York Kim, K. J. (2003). Financial time series forecasting using support vector machines. Neurocomputing 55 307–319 Kim, H. J. and Shin, K. S. (2007). A hybrid approach based on neural networks and genetic algorithms for detecting temporal patterns in stock markets. Applied Soft Computing 7 569–576 Lavielle, M. and Moulines, E. (2000). Leastsquares estimation of an unknown number of shifts in a time series. Journal of Time Series Analysis 21 33–59 Lebarbier, E. (2005). Detecting multiple changepoints in the mean of Gaussian process by model selection. Signal Processing 85 717–736 Lee, C. B. (1995). Estimating the number of change points in a sequence of independent normal random variables. Statistics & Probability Letters 25 241–248 Leitch, G. and Tanner, J. E. (1991). Economic forecast evaluation: Profits versus the conventional error measures. American Economic Review 81 580–590 Nason, G. P. (2008). Wavelet Methods in Statistics with R. Springer Nason, G. P., von Sachs, R. and Kroisandt, G. (2000). Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. Journal of the Royal Statistical Society: Series B 62 271292 NBER (2013). US Business Cycle Expansions and Contractions. National Bureau of Economic Research Ombao, H., Raz, J., von Sachs, R. and Guo, W. (2002). The SLEX model of a nonstationary random process. Annals of the Institute of Statistical Mathematics 54 171–200 Pan, J. and Chen, J. (2006). Application of modified information criterion to multiple change point problems. Journal of Multivariate Analysis 97 2221–2241 Priestley, M. B. (1983). Spectral Analysis and Time Series. Academic Press Spokoiny, V. (2009). Multiscale local change point detection with applications to valueatrisk. Annals of Statistics 37 1405–1436 Timmermans, C., Delsol, L. and von Sachs, R. (2012). Using Bagidis in nonparametric functional data analysis: Predicting from curves with sharp local features. Journal of Multivariate Analysis 115 421– 444 Cizek, P., Härdle, W. and Spokoiny, V. (2009). Adaptive pointwise estimation in timeinhomogeneous conditional heteroscedasticity models. Econometrics Journal 12 248–271 Venkatraman, E. S. (1992). Consistency results in multiple changepoint problems. PhD thesis, Department of Statistics, Stanford University Vidakovic, B. (2009). Statistical Modeling by Wavelets. John Wiley & Sons Vostrikova, L. (1981). Detecting ‘disorder’ in multidimensional random processes. Soviet Mathematics Doklady 24 55–59 Yao, Y. C. and Au, S. T. (1989). Leastsquares estimation of a step function. Sankhya: The Indian Journal of Statistics Series A 51 370–381 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/52379 