On the Nonlinear Predictability of Stock Returns Using Financial and Economic Variables.(Statistical Data Included)

In a recent article by Qi, neural networks trained by Bayesian regularization were used to predict excess returns on the S&P 500. The article concluded that the switching portfolio based on the recursive neural-network forecasts generates higher accumulated wealth with lower risks than that based on linear regression. Unfortunately, attempts to replicate the results were unsuccessful. Replicated results using the same software, approach and data detailed by Qi indicate that, in fact, the switching portfolio based on the recursive neural-network forecasts generates lower accumulated wealth with higher risks than that based on linear regression.

KEY WORDS: Minimization; Neural networks; Recursive prediction; Stock returns.

1. OVERVIEW

In a recent article, Qi (1999) provided a rich comparison of the within- and out-of-sample performance of recursive predictions of excess returns on the S&P 500 generated with linear regression (LR) and neural-network (NN) models. The main conclusions reported in the article were that NN's trained via Bayesian regularization outperform linear regression models in this context both within and out of sample. This dataset was also used by Pesaran and Timmermann (1995) and is one of the most widely studied time series in finance; therefore, these results are of interest to a wide audience.

In the course of modeling this dataset using competing nonlinear models, Maasoumi and Racine (2000) found that no model could come close to generating the level of accumulated wealth reported by Qi (1999) even though some of the competing models performed quite similarly in terms of their within- and out-of-sample performance. Unfortunately, the original Matlab code that was used to generate the reported results could not be located, while all attempts to replicate the results reported …