Empirical Evidence of Nonlinearity and Chaos in the Returns of American Depository Receipts

This paper examines the time series behavior of the returns of American depository receipts, ADRs. We postulate that the unique characteristics of these financial instruments make the ADR returns exhibit time series properties that are different from that of the U.S. equity market as a whole. Variance ratio tests of linear dependence reject the null hypothesis of random walk for the ADR returns. Tests based on the correlation dimension and the BDS statistic indicate the presence of nonlinearity in the ADR data. The BDS statistic applied to the standardized residuals of the EGARCH model rejects the null hypothesis that the data are independently and identically distributed, suggesting that conditional heteroskedasticity is not the cause of nonlinear structure in the data. On the other hand, tests of chaos, based on the locally weighted regression indicate that ADR returns exhibit chaotic behavior. This finding differs from previous research, which has failed to report evidence of chaos in the time series of American stock returns. Important contributions of this paper are the findings of statistically significant evidence of nonlinearity and low deterministic chaotic behavior in ADR returns. These results are important because knowing that returns of ADRs exhibit chaotic behavior can help us to understand this sector of the market better and find ways of predicting returns. In this respect our results also have practical implications, because they suggest that pricing forecasting models for ADR returns should include some nonlinear terms.