Comparative Analyses of Stock Returns Properties and Predictability

Abstract

This study investigates the stock returns of the Dow Jones Industrial Average (DJIA), Standard and Poor's (S&P) 500, and the National Association of Securities Dealers Automated Quotations (NASDAQ) to analyze and compare their properties and to determine their relative predictability. While it is commonly accepted that price per earnings ratio and corporate earnings are the main determinants of stock market returns, this assertion may not hold equally for monthly and daily stock returns. In addition, does this assertion hold equally for stock returns regardless of the stock market index? This work uses nonparametric spectral estimation to study the underlying properties of stock returns and uses monthly corporate earnings (corporate profits after tax) and 3-month Treasury bill interest rate (proxy for price per earnings ratio) to forecast the monthly stock returns of S&P 500, DJIA, and NASDAQ indices. Since corporate earnings are issued quarterly, this data set had to be interpolated to produce the monthly corporate earnings. Overall, the analyses and forecasting were facilitated with both statistical and digital signal processing techniques. Some examples of the techniques used include Hurst exponent to determine predictability, nonparametric spectral estimation to determine the underlying properties of the stock returns, and correlation and root mean square error to determine the forecasting accuracy. The results of this study provide evidence to support that economic and financial time series such as interest rates, corporate earnings, and stock market returns are time varying and nonGaussian with smooth compactly supported and essentially bandlimited power spectral density estimates. It further shows that the forecasts of the different stock market returns align well with the desired values and the S&P 500 forecasted stock returns were the best.