The ability to predict stock price changes, based on a given set of information, lies behind the notion of stock market efficiency. To the extent that lower efficiency is manifested as greater predictability in stock price changes, market efficiency is of practical interest to market participants who desire to "beat the market." In this dissertation nonlinearities are studied to uncover and illustrate some subtle aspects of stock market efficiency. The first chapter introduces the dissertation. The second and third chapters explore the (weak-form) efficient market hypothesis of predictability of stock price changes given the information inherent in the history of prices or returns. Chapter two studies the role of contemporaneous aggregation of securities in forming stock market indices such as the SP 500, to see if the recent findings of long-memory in the volatility of such indices can arise from the process of building an index. The presence of dependence in the volatility of return series lends predictability to the volatility representation of the return series, even over long spans of time. It is shown, theoretically, through simulations, and empirically, that the process of contemporaneous aggregation can lead to a long-memory finding in the volatility of returns. However, it is unlikely that this is the sole source of long memory, since there is also considerable evidence of long-memory in the volatility of individual return series. The third chapter seeks to uncover whether firm-specific characteristics have any impact on the long-memory finding in the volatility of U.S. stock returns. Empirical regularities in the relationship between the dependence in the volatility of returns and firm- specific characteristics are discovered. The fourth chapter analyzes nonlinear threshold relationships between nominal stock returns (in levels) and inflation. It is shown that the null of a linear relationship between nominal returns and inflation is rejected against threshold alternatives for most countries. The qualitative aspects of the estimated linear and threshold relationships for low-average-inflation countries are similar across countries, and the qualitative characteristics of these relationships are also similar among the high-average-inflation countries. The last chapter concludes the dissertation with recommendations for future research.
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