A Non-parametric Test and Predictive Model for Signed Path Dependence

While several tests for serial correlation in financial markets have been proposed and applied successfully in the literature, such tests provide rather limited information to construct predictive econometric models. This manuscript addresses this gap by providing a model-free definition of signed path dependence based on how the sign of cumulative innovations for a given lookback horizon correlates with the future cumulative innovations for a given forecast horizon. Such concept is then theoretically validated on well-known time series model classes and used to build a predictive econometric model for future market returns, which is applied to empirical forecasting by means of a profit-seeking trading strategy. The empirical experiment revealed strong evidence of serial correlation of unknown form in equity markets, being statistically significant and economically significant even in the presence of trading costs. Moreover, in equity markets, given a forecast horizon of one day, the forecasting strategy detected the strongest evidence of signed path dependence; however, even for longer forecast horizons such as 1 week or 1 month the strategy still detected such evidence albeit to a lesser extent. Currency markets also presented statistically significant serial dependence across some pairs, though not economically significant under the trading formulation presented.