Testing for Long-memory and Chaos in the Returns of Currency Exchange-traded Notes (ETNs)

The study uses autoregressive fractionally integrated moving average - fractionally integrated generalized autoregressive conditional heteroskedasticity (ARFIMA-FIGARCH) models and chaos effects to determine nonlinearity properties present on currency ETN returns. The results find that the volatilities of currency ETNs have long-memory, non-stationarity and non-invertibility properties. These findings make the research conclude that mean reversion is a possibility and that the efficient market hypothesis of Fama (1970) became ungrounded on these investment instruments. For the chaos effect, the BDS test finds that ETN returns and ARMA residuals also exhibit random processes, making conventional linear methodologies not appropriate for their analysis. The R/S analysis shows that currency ETN returns, ARMA and GARCH residuals have chaotic properties and are trend-reinforcing series. On the other hand, the correlation dimension analyses further confirmed that the utilized time-series have deterministic chaos properties. Thus, investors trying to predict returns and volatility of currency ETNs would fail to produce accurate findings because of their unstable structures, confirming their non-linear properties.