Neural Networks Approach to the Random Walk Dilemma of Financial Time Series

Predictions of financial time series often show a characteristic one step shift relative to the original data as in a random walk. This has been the cause for opposing views whether such time series do contain information that can be extracted for predictions, or are simply random walks. In this case study, we show that NNs that are capable of extracting weak low frequency periodic signals buried in a strong high frequency signal, consistently predict the next value in the series to be the current value, as in a random walk, when used for one-step-ahead predictions of the detrended S&P 500 time series. In particular for the Time Delay Feed Forward Networks and Elman Networks of various configurations, our study supports the view of the detrended S&P 500 being a random walk series. This is consistent with the long standing hypothesis that some financial time series are random walk series.