Abstract
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.
Highlights
The arrival of new information into asset price formation has been subject of extensive discussion
The seminal work in Fama (1970) has subsequently provided the definition of three forms of financial market efficiency: weak, where information contained in past prices is fully reflected in current prices; semi-strong, where all public information available is fully reflected in current prices; and strong, where all public and private information available is fully reflected in current prices
Such school of thought has evolved considerably and several different tests have been developed; it is still common practice to focus on the serial dependence of asset price changes to test for market efficiency, with a notable recent example seen in Urquhart and McGroarty (2016)
Summary
The arrival of new information into asset price formation has been subject of extensive discussion. We remark that some studies claim that apparent trend-following profits might not be arising out of positive serial correlation in returns but possibly out of intermediate horizon price performance (Novy-Marx 2012) or exogenous factors such as the presence of informed trading (Chena and Huainan 2012) or imbalances in liquidity and transaction costs (Lesmonda et al 2004) In such cases, the use of time series models will not yield significant benefits to an investor, as claimed in Banerjee and Hung (2013). As with any time series, its behaviour can abruptly change due to exogenous reasons; it is a common problem that can possibly reduce the usability of time series models, even though the tuning scheme based on a rolling observation window used in the calibration of the predictive model hereby proposed can alleviate this problem by readapting the model to most recent data and leaving obsolete data out of the fitted model
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