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Detecting Co-Movements in Noncausal Time Series

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Abstract
This paper introduces the notion of common noncausal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co-movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the noncausal (i.e. forward-looking) component of the series. In particular, we show that the presence of a reduced rank structure allows to identify purely causal and noncausal VAR processes of order two and higher even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can still be applied, where both lags and leads are used as instruments to determine whether the common features are present in either the backward-or forward-looking dynamics of the series. The proposed definitions of co-movements also valid for the mixed causal-noncausal VAR, with the exception that an approximate non-Gaussian maximum likelihood estimator is necessary for these cases. This means however that one loses the benefits of the simple tools proposed in this paper. An empirical analysis on European Brent and U.S. West Texas Intermediate oil prices illustrates the main findings. Whereas we fail to find any short run co-movements in a conventional causal VAR, they are detected in the growth rates of the series when considering a purely noncausal VAR.

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  • Gianluca Cubadda & Alain Hecq & Sean Telg, 2018. "Detecting Co-Movements in Noncausal Time Series," CEIS Research Paper 430, Tor Vergata University, CEIS, revised 23 Apr 2018.
    • Handle: RePEc:rtv:ceisrp:430
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    Cited by:

    1. Gianluca Cubadda & Alain Hecq, 2021. "Reduced Rank Regression Models in Economics and Finance," CEIS Research Paper 525, Tor Vergata University, CEIS, revised 08 Nov 2021.
    2. Gianluca Cubadda & Alain Hecq & Elisa Voisin, 2023. "Detecting Common Bubbles in Multivariate Mixed Causal–Noncausal Models," Econometrics, MDPI, vol. 11(1), pages 1-16, March.
    3. Alain Hecq & Elisa Voisin, 2023. "Predicting Crashes in Oil Prices During The Covid-19 Pandemic with Mixed Causal-Noncausal Models," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 209-233, Emerald Group Publishing Limited.
    4. Alain Hecq & Daniel Velasquez-Gaviria, 2022. "Spectral estimation for mixed causal-noncausal autoregressive models," Papers 2211.13830, arXiv.org.

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    More about this item

    Keywords

    causal and noncausal process; common features; vector autoregressive models; oil prices;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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