How to Identify Varying Lead-Lag Effects in Time Series Data: Implementation, Validation, and Application of the Generalized Causality Algorithm

This paper develops the generalized causality algorithm and applies it to a multitude of data from the fields of economics and finance. Specifically, our parameter-free algorithm efficiently determines the optimal non-linear mapping and identifies varying lead–lag effects between two given time series. This procedure allows an elastic adjustment of the time axis to find similar but phase-shifted sequences—structural breaks in their relationship are also captured. A large-scale simulation study validates the outperformance in the vast majority of parameter constellations in terms of efficiency, robustness, and feasibility. Finally, the presented methodology is applied to real data from the areas of macroeconomics, finance, and metal. Highest similarity show the pairs of gross domestic product and consumer price index (macroeconomics), S&P 500 index and Deutscher Aktienindex (finance), as well as gold and silver (metal). In addition, the algorithm takes full use of its flexibility and identifies both various structural breaks and regime patterns over time, which are (partly) well documented in the literature.

[1]  Didier Sornette,et al.  Non-parametric determination of real-time lag structure between two time series: the ‘optimal thermal causal path’ method , 2004, cond-mat/0408166.

[2]  J. Stübinger,et al.  Statistical Arbitrage with Mean-Reverting Overnight Price Gaps on High-Frequency Data of the S&P 500 , 2019, Journal of Risk and Financial Management.

[3]  Michael Grottke,et al.  Exploiting social media with higher-order Factorization Machines: statistical arbitrage on high-frequency data of the S&P 500 , 2018, Quantitative Finance.

[4]  J. Geweke,et al.  Optimal Prediction Pools , 2008 .

[5]  T. Gasser,et al.  Alignment of curves by dynamic time warping , 1997 .

[6]  Symmetric thermal optimal path and time-dependent lead-lag relationship: novel statistical tests and application to UK and US real-estate and monetary policies , 2014, 1408.5618.

[7]  D. McFadden,et al.  MIXED MNL MODELS FOR DISCRETE RESPONSE , 2000 .

[8]  Sangit Chatterjee,et al.  On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index , 1988 .

[9]  E. Mendoza,et al.  How Big (Small?) are Fiscal Multipliers? , 2010, SSRN Electronic Journal.

[10]  Philip Chan,et al.  Toward accurate dynamic time warping in linear time and space , 2007, Intell. Data Anal..

[11]  Thomas D. Gauthier,et al.  Detecting Trends Using Spearman's Rank Correlation Coefficient , 2001 .

[12]  B.-H. Juang,et al.  On the hidden Markov model and dynamic time warping for speech recognition — A unified view , 1984, AT&T Bell Laboratories Technical Journal.

[13]  Jiang Jiang,et al.  A Bayesian approach for sleep and wake classification based on dynamic time warping method , 2017, Multimedia Tools and Applications.

[14]  The Application of Dynamic Time Warping to the Quality Evaluation of Radix Puerariae thomsonii: Correcting Retention Time Shift in the Chromatographic Fingerprints. , 2015, Journal of chromatographic science.

[15]  C. Krauss,et al.  Statistical arbitrage with vine copulas , 2018 .

[16]  Massimiliano Marcellino,et al.  Midas Vs. Mixed-Frequency VAR: Nowcasting GDP in the Euro Area , 2009 .

[17]  E. Ghysels,et al.  Macroeconomics and the Reality of Mixed Frequency Data , 2015 .

[18]  Ali Shojaie,et al.  Network granger causality with inherent grouping structure , 2012, J. Mach. Learn. Res..

[19]  F. Itakura,et al.  Minimum prediction residual principle applied to speech recognition , 1975 .

[20]  Johannes Stübinger,et al.  Pairs trading with a mean-reverting jump–diffusion model on high-frequency data , 2018 .

[21]  J. Bai,et al.  Estimation of a Change Point in Multiple Regression Models , 1997, Review of Economics and Statistics.

[22]  Aaron E. Rosenberg,et al.  Performance tradeoffs in dynamic time warping algorithms for isolated word recognition , 1980 .

[23]  P. Perron,et al.  Computation and Analysis of Multiple Structural-Change Models , 1998 .

[24]  Xiaojing Xi,et al.  Capturing the Regime-Switching and Memory Properties of Interest Rates , 2014 .

[25]  Yanlin Shi,et al.  Markov Regime-Switching in-Mean Model with Tempered Stable Distribution , 2020, Computational Economics.

[26]  John Chamberlain,et al.  Tools for Validating Causal and Predictive Claims in Social Science Models , 2015 .

[27]  Tarik Arici,et al.  Robust gesture recognition using feature pre-processing and weighted dynamic time warping , 2014, Multimedia Tools and Applications.

[28]  Tianyou Chai,et al.  Dynamic time warping based causality analysis for root-cause diagnosis of nonstationary fault processes , 2015 .

[29]  Chi Xie,et al.  Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree , 2012 .

[30]  Michael A. West,et al.  Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting , 2017 .

[31]  Q Li,et al.  Dynamic time warping and machine learning for signal quality assessment of pulsatile signals , 2012, Physiological measurement.

[32]  Johannes Stübinger,et al.  Statistical arbitrage with optimal causal paths on high-frequency data of the S&P 500 , 2018, Quantitative Finance.

[33]  J. Stübinger,et al.  Epidemiology of Coronavirus COVID-19: Forecasting the Future Incidence in Different Countries , 2020, Healthcare.

[34]  Ophélie Fovet,et al.  Identifying seasonal patterns of phosphorus storm dynamics with dynamic time warping , 2015 .

[35]  Manfred Mudelsee,et al.  Estimating Pearson's Correlation Coefficient with Bootstrap Confidence Interval from Serially Dependent Time Series , 2003 .

[36]  Johannes Stübinger,et al.  A flexible regime switching model with pairs trading application to the S&P 500 high-frequency stock returns , 2019, Quantitative Finance.

[37]  D. Baur,et al.  The long-run relationship of gold and silver and the influence of bubbles and financial crises , 2013 .

[38]  Charles M. C. Lee,et al.  Accounting valuation, market expectation, and cross-sectional stock returns , 1998 .

[39]  Mike West,et al.  Dynamic Bayesian predictive synthesis in time series forecasting , 2016, Journal of Econometrics.

[40]  Didier Sornette,et al.  Non-parametric determination of real-time lag structure between two time series: The "optimal thermal causal path" method with applications to economic data , 2006 .

[41]  Hong Cheng,et al.  An image-to-class dynamic time warping approach for both 3D static and trajectory hand gesture recognition , 2016, Pattern Recognit..

[42]  J. Tobin.  Asian financial crisis , 1998 .

[43]  William N. Goetzmann,et al.  Pairs Trading: Performance of a Relative Value Arbitrage Rule , 1998 .

[44]  Eamonn J. Keogh,et al.  Exact indexing of dynamic time warping , 2002, Knowledge and Information Systems.

[45]  Jun Heo,et al.  Time series regression-based pairs trading in the Korean equities market , 2017, J. Exp. Theor. Artif. Intell..

[46]  Andrii Babii,et al.  Machine Learning Time Series Regressions With an Application to Nowcasting , 2019, Journal of Business & Economic Statistics.

[47]  C. Myers,et al.  A level building dynamic time warping algorithm for connected word recognition , 1981 .

[48]  S. Chiba,et al.  Dynamic programming algorithm optimization for spoken word recognition , 1978 .