The use of Neural Networks for modeling nonlinear mean reversion: Measuring efficiency and integration in ADR markets

We propose the use of a Neural Network (NN) methodology for evaluating models of time series that exhibit nonlinear mean reversion, such as those stemming from equilibrium relationships that are affected by transaction costs or institutional rigidities. Given the vast array of such models found in the literature, the proposed NN procedure represents a useful graphical tool, providing the researcher with the ability to visualize the data before choosing the most appropriate approach for modeling mean-reversion dynamics with either a Threshold Autoregression (TAR), a Smooth Transition Autoregression (STAR), or any hybrid model. Our case study is involved with understanding the nature of cross-listed stocks (ADRs) and the degree of market integration and efficiency, as captured by the NN methodology. This is done through an analysis of the intradaily price discrepancies of cross-listed French, Mexican and American stocks. The results of the NN methodology are relevant in describing the arbitrage forces that maintain the Law of One Price in these ADR markets, and thus provide a more explicit insight on how these markets are integrated.