Efficient market model: within-sample fit versus out-of-sample forecasts

Abstract

In this paper, we study whether the pricing of index futures and the underlying cash prices are efficient. Price efficiency per se is not testable. It must be tested jointly with a maintained model. The topic of time series model specification has been the center of considerable attention in the applied econometric literature. The criterion Predictive Least Squares (PLS) based on actual postsample forecasting performance is proposed to identify a time series model. The criterion is applied to the S&P 500 stock prices. Its performance is compared to the well-known methods, the Bayesian Information Criterion (BIC) and Final Prediction Error (FPE), which are based on within-sample fit. We follow standard time series modeling procedures of testing for data stationarity, univariate model specification, bivariate model specification, testing for cointegration, and error correction model representation. The Root Mean Squared Forecast Errors (RMSFE) on the alternative models are investigated and the significance level between different models is discussed. At the 20% significance level cash prices and futures prices are generated in efficient markets, as the random walk models, specified by PLS, result in significantly lower RMSFE relative to the non-random walk models specified by FPE. Different criteria lead to different conclusions. Whether a market is efficient seems to depend on the criterion we used to specify model, thus the criterion used to select the model is important. As the rule of parsimony seeks simple models which predict well, PLS appears to be a worthy candidate for further consideration.