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A Simple Test for Causality in Volatility

Author

Listed:
  • Chia-Lin Chang

    (National Chung Hsing University, Taiwan)

  • Michael McAleer

    (National Tsing Hua University, Taiwan; Erasmus University Rotterdam, The Netherlands, Complutense University of Madrid, Spain, Yokohama National University, Japan)

Abstract
An early development in testing for causality (technically, Granger non-causality) in the conditional variance (or volatility) associated with financial returns, was the portmanteau statistic for non-causality in variance of Cheng and Ng (1996). A subsequent development was the Lagrange Multiplier (LM) test of non-causality in the conditional variance by Hafner and Herwartz (2006), who provided simulations results to show that their LM test was more powerful than the portmanteau statistic. While the LM test for causality proposed by Hafner and Herwartz (2006) is an interesting and useful development, it is nonetheless arbitrary. In particular, the specification on which the LM test is based does not rely on an underlying stochastic process, so that the alternative hypothesis is also arbitrary, which can affect the power of the test. The purpose of the paper is to derive a simple test for causality in volatility that provides regularity conditions arising from the underlying stochastic process, namely a random coefficient autoregressive process, and for which the (quasi-) maximum likelihood estimates have valid asymptotic properties. The simple test is intuitively appealing as it is based on an underlying stochastic process, is sympathetic to Granger’s (1969, 1988) notion of time series predictability, is easy to implement, and has a regularity condition that is not available in the LM test.

Suggested Citation

  • Chia-Lin Chang & Michael McAleer, 2016. "A Simple Test for Causality in Volatility," Tinbergen Institute Discussion Papers 16-094/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20160094
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    References listed on IDEAS

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    Cited by:

    1. Michael mcAleer, 2017. "Stationarity and Invertibility of a Dynamic Correlation Matrix," Tinbergen Institute Discussion Papers 17-082/III, Tinbergen Institute.
    2. Chia-Lin Chang & Michael McAleer & Chien-Hsun Wang, 2017. "An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors," IJFS, MDPI, vol. 6(1), pages 1-24, December.
    3. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2017. "Realized stochastic volatility with general asymmetry and long memory," Journal of Econometrics, Elsevier, vol. 199(2), pages 202-212.
    4. Chia-Lin Chang & Michael McAleer & Guangdong Zuo, 2017. "Volatility Spillovers and Causality of Carbon Emissions, Oil and Coal Spot and Futures for the EU and USA," Sustainability, MDPI, vol. 9(10), pages 1-22, October.
    5. Alessandra Amendola & Marinella Boccia & Vincenzo Candila & Giampiero M. Gallo, 2020. "Energy and non–energy Commodities: Spillover Effects on African Stock Markets," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 9(4), pages 1-7.
    6. Vincenzo Candila & Salvatore Farace, 2018. "On the Volatility Spillover between Agricultural Commodities and Latin American Stock Markets," Risks, MDPI, vol. 6(4), pages 1-16, October.
    7. Duc Hong Vo & Tan Ngoc Vu & Anh The Vo & Michael McAleer, 2019. "Modeling the Relationship between Crude Oil and Agricultural Commodity Prices," Energies, MDPI, vol. 12(7), pages 1-41, April.
    8. Kim, Rebecca Chunghee & Yoo, Kate Inyoung & Uddin, Helal, 2018. "The Korean Air nut rage scandal: Domestic versus international responses to a viral incident," Business Horizons, Elsevier, vol. 61(4), pages 533-544.
    9. Yuki Toyoshima, 2018. "Testing for Causality-In-Mean and Variance between the UK Housing and Stock Markets," JRFM, MDPI, vol. 11(2), pages 1-10, April.
    10. Chang, Chia-Lin & McAleer, Michael & Wang, Yu-Ann, 2018. "Modelling volatility spillovers for bio-ethanol, sugarcane and corn spot and futures prices," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 1002-1018.
    11. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    12. Muhammad Irfan Malik & Abdul Rashid, 2017. "Return And Volatility Spillover Between Sectoral Stock And Oil Price: Evidence From Pakistan Stock Exchange," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 1-22, June.
    13. Hamermesh, Daniel S. & Pfann, Gerard A., 2022. "The variability and volatility of sleep: An ARCHetypal behavior," Economics & Human Biology, Elsevier, vol. 47(C).
    14. Pavel Kotyza & Katarzyna Czech & Michał Wielechowski & Luboš Smutka & Petr Procházka, 2021. "Sugar Prices vs. Financial Market Uncertainty in the Time of Crisis: Does COVID-19 Induce Structural Changes in the Relationship?," Agriculture, MDPI, vol. 11(2), pages 1-16, January.
    15. Miles, Sandra Jeanquart & McCamey, Randy, 2018. "The candidate experience: Is it damaging your employer brand?," Business Horizons, Elsevier, vol. 61(5), pages 755-764.
    16. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.

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    More about this item

    Keywords

    Random coefficient stochastic process; Simple test; Granger non-causality; Regularity conditions; Asymptotic properties; Conditional volatility;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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