Analysis of ultra-high-frequency financial data using advanced Fourier transforms

This paper presents a novel application of advanced methods from Fourier analysis to the study of ultra-high-frequency financial data. The use of Lomb-Scargle Fourier transform, provides a robust framework to take into account the irregular spacing in time, minimising the computational effort. Likewise, it avoids complex model specifications (e.g. ACD or intensity models) or resorting to traditional methods, such as (linear or cubic) interpolation and regular resampling, which not only cause artifacts in the data and loss of information, but also lead to the generation and use of spurious information.

[1]  R. Gencay,et al.  An Introduc-tion to High-Frequency Finance , 2001 .

[2]  Luc Bauwens,et al.  Stochastic Conditional Intensity Processes , 2006 .

[3]  Gordon J. F. MacDonald,et al.  Ice Ages and Astronomical Causes: Data, Spectral Analysis and Mechanisms , 2002 .

[4]  Richard A. Davis,et al.  Handbook of Financial Time Series , 2009 .

[5]  Trades and Quotes: A Bivariate Point Process , 1998 .

[6]  W. D. Ray,et al.  Spectral Analysis and Time Series. Vol. 1: Univariate Series. , 1982 .

[7]  C. Granger,et al.  Applications of spectral analysis in econometrics , 1983 .

[8]  Luc Bauwens,et al.  A Comparison of Financial Duration Models Via Density Forecast , 2004 .

[9]  N. Lomb.  Least-squares frequency analysis of unequally spaced data , 1976 .

[10]  J. Scargle.  Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data , 1989 .

[11]  A. Izenman,et al.  Fourier Analysis of Time Series: An Introduction , 1977, IEEE Transactions on Systems, Man and Cybernetics.

[12]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[13]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[14]  Jeffrey R. Russell,et al.  Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data , 1998 .

[15]  Maureen O'Hara,et al.  Market Microstructure Theory , 1995 .

[16]  N. Wermuth,et al.  Nonlinear Time Series: Nonparametric and Parametric Methods , 2005 .

[17]  J. Grammig,et al.  Trading Activity and Liquidity Supply in a Pure Limit Order Book Market. An Empirical Analysis Using a Multivariate Count Data Model , 2004 .

[18]  Eric R. Ziegel,et al.  Spectral Analysis of Time-series Data , 2004, Technometrics.

[19]  J. Scargle.  Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data , 1982 .

[20]  M. Pamela Griffin,et al.  Comparison and Clinical Application of Frequency Domain Methods in Analysis of Neonatal Heart Rate Time Series , 2001, Annals of Biomedical Engineering.

[21]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[22]  Peter Bloomfield,et al.  Fourier Analysis of Time Series: An Introduction , 1977 .

[23]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[24]  G. Moody,et al.  Power spectral density of unevenly sampled data by least-square analysis: performance and application to heart rate signals , 1998, IEEE Transactions on Biomedical Engineering.

[25]  Antony Ware,et al.  Fast Approximate Fourier Transforms for Irregularly Spaced Data , 1998, SIAM Rev..

[26]  M. Di Rienzo,et al.  On the evaluation of heart rate spectra: the Lomb periodogram , 1996, Computers in Cardiology 1996.

[27]  Thomas Ruf,et al.  The Lomb-Scargle Periodogram in Biological Rhythm Research: Analysis of Incomplete and Unequally Spaced Time-Series , 1999 .

[28]  W. Press,et al.  Fast algorithm for spectral analysis of unevenly sampled data , 1989 .

[29]  Maureen O'Hara,et al.  Time and the Process of Security Price Adjustment , 1992 .

[30]  Rebecca M. Warner,et al.  Spectral Analysis of Time-Series Data , 1998 .

[31]  P. A. Blight.  The Analysis of Time Series: An Introduction , 1991 .

[32]  S. Baliunas,et al.  A Prescription for period analysis of unevenly sampled time series , 1986 .

[33]  Nikolaus Hautsch,et al.  Order aggressiveness and order book dynamics , 2004 .

[34]  A. Iacobucci.  Spectral Analysis for Economic Time Series , 2005 .

[35]  Joachim Grammig,et al.  A family of autoregressive conditional duration models , 2006 .

[36]  Michael Schulz,et al.  Spectrum: spectral analysis of unevenly spaced paleoclimatic time series , 1997 .

[37]  H P Van Dongen,et al.  A procedure of multiple period searching in unequally spaced time-series with the Lomb-Scargle method. , 1999, Biological rhythm research.

[38]  Jie Chen,et al.  Bioinformatics Original Paper Detecting Periodic Patterns in Unevenly Spaced Gene Expression Time Series Using Lomb–scargle Periodograms , 2022 .

[39]  Luc Bauwens,et al.  Département des Sciences Économiques de l'Université catholique de Louvain Modelling Financial High Frequency Data Using Point Processes , 2019 .