Improving model performance with the integrated wavelet denoising method

Abstract Intelligent pattern recognition imposes new challenges in high-frequency financial data mining due to its irregularities and roughness. Based on the wavelet transform for decomposing systematic patterns and noise, in this paper we propose a new integrated wavelet denoising method, named smoothness-oriented wavelet denoising algorithm (SOWDA), that optimally determines the wavelet function, maximal level of decomposition, and the threshold rule by using a smoothness score function that simultaneously detects the global and local extrema. We discuss the properties of our method and propose a new evaluation procedure to show its robustness. In addition, we apply this method both in simulation and empirical investigation. Both the simulation results based on three typical stylized features of financial data and the empirical results in analyzing high-frequency financial data from Frankfurt Stock Exchange confirm that SOWDA significantly (based on the RMSE comparison) improves the performance of classical econometric models after denoising the data with the discrete wavelet transform (DWT) and maximal overlap discrete wavelet transform (MODWT) methods.

[1]  Nikola Gradojevic,et al.  Errors-in-variables estimation with wavelets , 2009 .

[2]  Jianqing Fan,et al.  Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data , 2006 .

[3]  Edward W. Sun,et al.  High frequency trading, liquidity, and execution cost , 2013, Annals of Operations Research.

[4]  Emily K. Lada,et al.  A wavelet-based spectral procedure for steady-state simulation analysis , 2006, Eur. J. Oper. Res..

[5]  J. B. Ramsey,et al.  The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income , 1998 .

[6]  Thomas Meinl,et al.  A Nonlinear Filtering Algorithm based on Wavelet Transforms for High-Frequency Financial Data Analysis , 2012 .

[7]  Svetlozar T. Rachev,et al.  Analysis of the intraday effects of economic releases on the currency market , 2011 .

[8]  Todd R. Ogden,et al.  Wavelet Methods for Time Series Analysis , 2002 .

[9]  Fritz Keinert,et al.  Wavelets and Multiwavelets , 2003 .

[10]  Alexander Shapiro,et al.  Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics , 2012, Oper. Res..

[11]  Patrick M. Crowley,et al.  A Guide to Wavelets for Economists , 2007 .

[12]  Emmanuel Haven,et al.  De-noising option prices with the wavelet method , 2012, Eur. J. Oper. Res..

[13]  Thomas Meinl,et al.  A new wavelet-based denoising algorithm for high-frequency financial data mining , 2012, Eur. J. Oper. Res..

[14]  James B. Ramsey,et al.  Wavelets in Economics and Finance: Past and Future , 2002 .

[15]  Brandon Whitcher,et al.  Systematic risk and timescales , 2003 .

[16]  D. L. Kelly,et al.  Private Information and High-Frequency Stochastic Volatility , 2003 .

[17]  J. B. Ramsey,et al.  DECOMPOSITION OF ECONOMIC RELATIONSHIPS BY TIMESCALE USING WAVELETS , 1998, Macroeconomic Dynamics.

[18]  F. In,et al.  The Relationship Between Financial Variables and Real Economic Activity: Evidence From Spectral and Wavelet Analyses , 2003 .

[19]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Yanqin Fan,et al.  UNIT ROOT TESTS WITH WAVELETS , 2008, Econometric Theory.

[21]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[22]  S. Rachev,et al.  Multivariate Skewed Student's t Copula in the Analysis of Nonlinear and Asymmetric Dependence in the German Equity Market , 2008 .

[23]  Ramazan Gençay,et al.  Investment Horizon Effect on Asset Allocation between Value and Growth Strategies , 2010 .

[24]  P. Mykland,et al.  Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics , 2008 .

[25]  I. Johnstone,et al.  Minimax estimation via wavelet shrinkage , 1998 .

[26]  J. Morlet.  Sampling Theory and Wave Propagation , 1983 .

[27]  R. Gencay,et al.  Multiscale systematic risk , 2005 .

[28]  R. Gencay,et al.  An Introduction to Wavelets and Other Filtering Methods in Finance and Economics , 2001 .

[29]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[30]  Maria Joana Soares,et al.  The Yield Curve and the Macro-economy across Time and Frequencies" (Cef.up Working Paper nº. 2010-04, July 2010) , 2012 .

[31]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[32]  Ramazan Gençay,et al.  Jump detection with wavelets for high-frequency financial time series , 2014 .

[33]  Mercedes Esteban-Bravo,et al.  Computing continuous-time growth models with boundary conditions via wavelets , 2007 .

[34]  Mark J. Jensen.  An Alternative Maximum Likelihood Estimator of Long-Memeory Processes Using Compactly Supported Wavelets , 1997 .

[35]  P. Massart,et al.  Minimum contrast estimators on sieves: exponential bounds and rates of convergence , 1998 .

[36]  Wei Sun,et al.  A New Approach for Using Lévy Processes for Determining High-Frequency Value-at-Risk Predictions , 2009 .

[37]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[38]  Yongmiao Hong,et al.  Wavelet-Based Testing for Serial Correlation of Unknown Form in Panel Models , 2000 .

[39]  S. Rachev,et al.  Fractals or I.I.D.: Evidence of long-range dependence and heavy tailedness from modeling German equity market returns , 2007 .

[40]  D. Donoho.  Asymptotic minimax risk for sup-norm loss: Solution via optimal recovery , 1994 .

[41]  B. Silverman,et al.  Incorporating Information on Neighboring Coefficients Into Wavelet Estimation , 2001 .

[42]  Brandon Whitcher,et al.  Asymmetry of information flow between volatilities across time scales , 2009 .

[43]  Algirdas Laukaitis,et al.  Functional data analysis for cash flow and transactions intensity continuous-time prediction using Hilbert-valued autoregressive processes , 2008, Eur. J. Oper. Res..

[44]  Connor Jeff,et al.  Wavelet Transforms and Commodity Prices , 2005 .

[45]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[46]  Robert E. McCulloch,et al.  Nonlinearity in High-Frequency Financial Data and Hierarchical Models , 2001 .

[47]  F. E. Grubbs.  Procedures for Detecting Outlying Observations in Samples , 1969 .