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Wavelet multiple correlation and cross-correlation: A multiscale analysis of euro zone stock markets

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  • Fernández Macho, Francisco Javier

Abstract

Statistical studies that consider multiscale relationships among several variables use wavelet correlations and cross-correlations between pairs of variables. This procedure needs to calculate and compare a large number of wavelet statistics. The analysis can then be rather confusing and even frustrating since it may fail to indicate clearly the multiscale overall relationship that might exist among the variables. This paper presents two new statistical tools that help to determine the overall correlation for the whole multivariate set on a scale-by-scale basis. This is illustrated in the analysis of a multivariate set of daily Eurozone stock market returns during a recent period. Wavelet multiple correlation analysis reveals the existence of a nearly exact linear relationship for periods longer than the year, which can be interpreted as perfect integration of these Euro stock markets at the longest time scales. It also shows that small inconsistencies between Euro markets seem to be just short within-year discrepancies possibly due to the interaction of different agents with different trading horizons. On the other hand, multiple cross-correlation analysis shows that the French CAC40 may lead the rest of the Euro markets at those short time scales.

Suggested Citation

  • Fernández Macho, Francisco Javier, 2011. "Wavelet multiple correlation and cross-correlation: A multiscale analysis of euro zone stock markets," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    • Handle: RePEc:ehu:biltok:5575
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    More about this item

    Keywords

    Euro zone; MODWT; multiscale analysis; multivariate analysis; stock markets; returns; wavelet transform;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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