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Nonlinear causality testing with stepwise multivariate filtering


  • Stelios Bekiros


This study explores the direction and nature of causal linkages among six currencies denoted relative to United States dollar (USD), namely Euro (EUR), Great Britain Pound (GBP), Japanese Yen (JPY), Swiss Frank (CHF), Australian Dollar (AUD) and Canadian Dollar (CAD). These are the most liquid and widely traded currency pairs in the world and make up about 90% of total Forex trading worldwide. The data covers the period 3/20/1987-11/14/2007, including the Asian crisis, the dot-com bubble and the period just before the outbreak of the US subprime crisis. The objective of the paper is to test for the existence of both linear and nonlinear causal relationships among these currency markets. The modified Baek-Brock test for nonlinear non-causality is applied on the currency return time series as well as the linear Granger test. Further to the classical pairwise analysis causality testing is conducted in a multivariate formulation, to correct for the effects of the other variables. A new stepwise multivariate filtering approach is implemented. To check if any of the observed causality is strictly nonlinear, the nonlinear causal relationships of VAR/VECM filtered residuals are also examined. Finally, the hypothesis of nonlinear non-causality is investigated after controlling for conditional heteroskedasticity in the data using GARCH-BEKK, CCC-GARCH and DCC-GARCH models. Significant nonlinear causal linkages persisted even after multivariate GARCH filtering. This indicates that if nonlinear effects are accounted for, neither FX market leads or lags the other consistently and currency returns may exhibit statistically significant higher-order moments and asymmetries.

Suggested Citation

  • Stelios Bekiros, 2011. "Nonlinear causality testing with stepwise multivariate filtering," Economics Working Papers ECO2011/22, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2011/22

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    References listed on IDEAS

    1. Ramsey James B. & Lampart Camille, 1998. "The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(1), pages 1-22, April.
    2. Charles Engel & Kenneth D. West, 2005. "Exchange Rates and Fundamentals," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 485-517, June.
    3. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    4. Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon, 2001. "Differentiating intraday seasonalities through wavelet multi-scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 543-556.
    5. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters,in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230 National Bureau of Economic Research, Inc.
    6. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    7. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    8. van Dijk, Dick & Osborn, Denise R. & Sensier, Marianne, 2005. "Testing for causality in variance in the presence of breaks," Economics Letters, Elsevier, vol. 89(2), pages 193-199, November.
    9. Bekiros, Stelios D., 2010. "Heterogeneous trading strategies with adaptive fuzzy Actor-Critic reinforcement learning: A behavioral approach," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1153-1170, June.
    10. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    11. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, March.
    12. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 669-682.
    13. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    14. G. Wenchi Kao & Christopher K. Ma, 1992. "Memories, heteroscedasticity, and price limit in Currency futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 12(6), pages 679-692, December.
    15. Levich, Richard M. & Thomas, Lee III, 1993. "The significance of technical trading-rule profits in the foreign exchange market: a bootstrap approach," Journal of International Money and Finance, Elsevier, vol. 12(5), pages 451-474, October.
    16. Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
    17. Ma, Yue & Kanas, Angelos, 2000. "Testing for a nonlinear relationship among fundamentals and exchange rates in the ERM," Journal of International Money and Finance, Elsevier, vol. 19(1), pages 135-152, February.
    18. Yao, Feng & Hosoya, Yuzo, 2000. "Inference on one-way effect and evidence in Japanese macroeconomic data," Journal of Econometrics, Elsevier, vol. 98(2), pages 225-255, October.
    19. Bekiros, Stelios D., 2010. "Fuzzy adaptive decision-making for boundedly rational traders in speculative stock markets," European Journal of Operational Research, Elsevier, vol. 202(1), pages 285-293, April.
    20. Agnès Bénassy-Quéré & Amina Lahrèche-Révil, 2000. "The Euro as a Monetary Anchor in the CEECs," Open Economies Review, Springer, vol. 11(4), pages 303-321, October.
    21. Robert P. Flood & Peter Isard, 1989. "Monetary Policy Strategies," IMF Staff Papers, Palgrave Macmillan, vol. 36(3), pages 612-632, September.
    22. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    23. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    24. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    25. Wang, Zijun & Yang, Jian & Li, Qi, 2007. "Interest rate linkages in the Eurocurrency market: Contemporaneous and out-of-sample Granger causality tests," Journal of International Money and Finance, Elsevier, vol. 26(1), pages 86-103, February.
    26. Nikkinen, Jussi & Sahlstrom, Petri & Vahamaa, Sami, 2006. "Implied volatility linkages among major European currencies," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 16(2), pages 87-103, April.
    27. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    28. Black, Fischer, 1986. " Noise," Journal of Finance, American Finance Association, vol. 41(3), pages 529-543, July.
    29. Hiemstra, Craig & Jones, Jonathan D, 1994. " Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation," Journal of Finance, American Finance Association, vol. 49(5), pages 1639-1664, December.
    30. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    31. Engle, Robert F & Ito, Takatoshi & Lin, Wen-Ling, 1990. "Meteor Showers or Heat Waves? Heteroskedastic Intra-daily Volatility in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 58(3), pages 525-542, May.
    32. Breitung, Jorg & Candelon, Bertrand, 2006. "Testing for short- and long-run causality: A frequency-domain approach," Journal of Econometrics, Elsevier, vol. 132(2), pages 363-378, June.
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    Cited by:

    1. Nick, Sebastian, 2013. "Price Formation and Intertemporal Arbitrage within a Low-Liquidity Framework: Empirical Evidence from European Natural Gas Markets," EWI Working Papers 2013-14, Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI).
    2. Sebastian Nick, 2016. "The Informational Efficiency of European Natural Gas Hubs: Price Formation and Intertemporal Arbitrage," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).

    More about this item


    nonparametric Granger causality; filtering; multivariate GARCH models; spillovers;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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