An Intuitive Guide to Wavelets for Economists

Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not yet fully entered the economics discipline. In this discussion paper, wavelet analysis is introduced in an intuitive manner, and the existing economics and finance literature that utilises wavelets is explored. Extensive examples of exploratory wavelet analysis are given, many using Canadian, US and Finnish industrial production data. Finally, potential future applications for wavelet analysis in economics are also discussed and explored.

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

[2]  Andrew G. Bruce,et al.  WaveShrink: shrinkage functions and thresholds , 1995, Optics + Photonics.

[3]  O. Holter.  Wavelet Analysis of Time Series , 1995 .

[4]  Bernd Süssmuth.  National and Supranational Business Cycles (1960-2000): A Multivariate Description of Central G7 and Euro15 Nipa Aggregates , 2002, SSRN Electronic Journal.

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

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

[7]  P. Guttorp,et al.  Mathematical Background for Wavelet Estimators of Cross-Covariance and Cross-Correlation , 2022 .

[8]  Hong-Ye Gao,et al.  Applied wavelet analysis with S-plus , 1996 .

[9]  A. Bruce,et al.  S+Wavelets: Algorithms and Technical Details. , 1995 .

[10]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[11]  Nick G. Kingsbury,et al.  A dual-tree complex wavelet transform with improved orthogonality and symmetry properties , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[12]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[13]  A. H. Hallett,et al.  Spectral Analysis as a Tool for Financial Policy: An Analysis of the Short-End of the British Term Structure , 2004 .

[14]  F. Collard.  Spectral and persistence properties of cyclical growth , 1998 .

[15]  Peter Guttorp.  National Research Center for Statistics and the Environment , 2006 .

[16]  Ronald R. Coifman,et al.  Signal processing and compression with wavelet packets , 1994 .

[17]  C. Greenhall.  Recipes for degrees of freedom of frequency stability estimators , 1991 .

[18]  Mark J. Jensen.  Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter , 1997 .

[19]  P. Conway,et al.  A spectral analysis of New Zealand output gaps using Fourier and wavelet techniques , 2000 .

[20]  Nick G. Kingsbury,et al.  The dual-tree complex wavelet transform: A new efficient tool for image restoration and enhancement , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[21]  Ka-Ming Lau,et al.  Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing , 1995 .

[22]  Christoph Schleicher,et al.  An Introduction to Wavelets for Economists , 2002 .

[23]  Peter Guttorp,et al.  Multiscale detection and location of multiple variance changes in the presence of long memory , 2000 .

[24]  Hahn-Shik Lee.  International transmission of stock market movements: a wavelet analysis , 2004 .

[25]  Peter Guttorp,et al.  Wavelet analysis of covariance with application to atmospheric time series , 2000 .

[26]  P. Guttorp,et al.  Testing for homogeneity of variance in time series: Long memory, wavelets, and the Nile River , 2002 .

[27]  G. C. Tiao,et al.  Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance , 1994 .

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

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

[30]  James B. Ramsey,et al.  The contribution of wavelets to the analysis of economic and financial data , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[31]  D. Percival,et al.  Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets , 1997 .

[32]  V. Fernandez.  Time-Scale Decomposition of Price Transmission in International Markets , 2005 .

[33]  George Kapetanios,et al.  Spectral Based Methods to Identify Common Trends and Common Cycles , 2001, SSRN Electronic Journal.

[34]  I. Daubechies,et al.  Biorthogonal bases of compactly supported wavelets , 1992 .

[35]  B. Silverman,et al.  Wavelets: The Key to Intermittent Information? , 2000 .

[36]  Greg Tkacz,et al.  Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator , 2001 .

[37]  Enrico Capobianco,et al.  Multiscale Analysis of Stock Index Return Volatility , 2004 .

[38]  C. Greiber,et al.  Inflation and Core Money Growth in the Euro Area , 2004, SSRN Electronic Journal.

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

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

[41]  Michael R. Chernick,et al.  Wavelet Methods for Time Series Analysis , 2001, Technometrics.

[42]  Fionn Murtagh,et al.  Prediction Based on a Multiscale Decomposition , 2003, Int. J. Wavelets Multiresolution Inf. Process..

[43]  Tommi A. Vuorenmaa.  A Multiresolution Analysis of Stock Market Volatility Using Wavelet Methodology , 2004 .

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

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

[46]  Roy D. Wallen,et al.  The Illustrated Wavelet Transform Handbook , 2004 .

[47]  J. B. Ramsey,et al.  The analysis of foreign exchange data using waveform dictionaries , 1997 .

[48]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[49]  Mehmet Dalkir.  A new approach to causality in the frequency domain , 2004 .

[50]  James S. Walker,et al.  A Primer on Wavelets and Their Scientific Applications , 1999 .

[51]  Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator , 1994 .

[52]  J. V. E. Azevedo.  Business Cycles: Cyclical Comovement Within the European Union in the Period 1960-1999. A Frequency Domain Approach , 2002 .

[53]  K J Blinowska,et al.  Introduction to wavelet analysis. , 1997, British journal of audiology.

[54]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

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

[56]  Brandon J. Whitcher,et al.  Multivariate Spectral Analysis Using Hilbert Wavelet Pairs , 2004, Int. J. Wavelets Multiresolution Inf. Process..