Periodic Structure of Equity Market Annual Returns and Their Predictability

Abstract

The highly periodic nature of equity market annual returns is uncovered in examples of S&P 500 and Nasdaq. The period of oscillations is found to be (3.46 ± 0.47) years and (3.38 ± 0.38) years for those markets respectively with a 90% confidence level based on statistical analysis. The analytical oscillatory model, which works via a mean reversion mechanism that reverses the extreme values of returns to neutral and opposite ones, is introduced to explain such dynamics. While the autocorrelations of lag 1 and lag 2 are both rather small, -3.1% and -18.0%, the correlation between the acceleration term in the model’s main equation and the deviation from the mean turns out to be very high, 84.9%, which proves, based on the S&P 500 and Nasdaq data, that the market annual returns are indeed governed by the proposed pendulum-like stochastic difference equation. The Shapiro-Wilks and Kolmogorov-Smirnov tests both reject the normality hypothesis of the annual returns. We also introduce an oscillator indicator that reliably picks up periods of excess capital pumped in and out of the markets, signaling bubbles and crashes. The given oscillatory mechanism is used in conjunction with machine learning models, such as Elastic Net and Random Forest, to predict the behavior of the markets.

Keywords: Oscillator, indicator, market, prediction, machine learning, stock, finance, return, trading, strategy, equation