Long-Term Memory in Stock Market Prices

TLDR

The study develops a robust test for long‑run memory that accounts for short‑range dependence. The test extends Mandelbrot’s range‑over‑standard‑deviation (R/S) statistic, derives its asymptotic sampling theory via functional central limit theory, and is applied to daily, weekly, monthly, and annual stock‑return indices across multiple periods. The test finds no long‑range dependence in any index when short‑term autocorrelations are controlled, and Monte Carlo experiments show it can detect long‑run memory in two models, implying short‑range dependence models may suffice for stock‑return series.

Abstract

A test for long-run memory that is robust to short-range dependence is developed. It is a simple extension of Mandelbrot's range over standard deviation or R/S statistic, for which the relevant asymptotic sampling theory is derived via functional central limit theory. This test is applied to daily, weekly, monthly, and annual stock returns indexes over several different time periods. Contrary to previous findings, there is no evidence of long-range dependence in any of the indexes over any sample period or sub-period once short-term autocorrelations are taken into account. Illustrative Monte Carlo experiments indicate that the modified R/S test has power against at least two specific models of long-run memory, suggesting that stochastic models of short-range dependence may adequately capture the time series behavior of stock returns.