This paper examines whether stock prices for a sample of 22 OECD countries can be best represented as mean reversion or random walk processes. A sequential trend break test proposed by Zivot and Andrews is implemented, which has the advantage that it can take account of a structural break in the series, as well as panel data unit root tests proposed by Im et al., which exploits the extra power in the panel properties of the data. Results provide strong support for the random walk hypothesis.