Testing for Long-memory and Chaos in the Returns of Currency Exchange-traded Notes (ETNs)
John Francis Diaz and
Journal of Applied Finance & Banking, 2017, vol. 7, issue 4, 2
The study uses autoregressive fractionally integrated moving average â€“Â fractionally integrated generalized autoregressive conditional heteroskedasticityÂ (ARFIMA-FIGARCH) models and chaos effects to determine nonlinearityÂ properties present on currency ETN returns. The results find that the volatilitiesÂ of currency ETNs have long-memory, non-stationarity and non-invertibilityÂ properties. These findings make the research conclude that mean reversion is aÂ possibility and that the efficient market hypothesis of Fama (1970) becameÂ ungrounded on these investment instruments. For the chaos effect, the BDS testÂ finds that ETN returns and ARMA residuals also exhibit random processes,Â making conventional linear methodologies not appropriate for their analysis.Â The R/S analysis shows that currency ETN returns, ARMA and GARCH residualsÂ have chaotic properties and are trend-reinforcing series. On the other hand, theÂ correlation dimension analyses further confirmed that the utilized time-series haveÂ deterministic chaos properties. Thus, investors trying to predict returns andÂ volatility of currency ETNs would fail to produce accurate findings because ofÂ their unstable structures, confirming their non-linear properties.JEL classification numbers: G10, G15Keywords: Currency ETNs, Long-memory Properties, ARFIMA-FIGARCH,Â Chaos Effects.
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