Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns

Abstract

SUMMARYWe provide an empirical framework for assessing the distributional properties of daily speculative returns within the context of the continuous-time jump diffusion models traditionally used in asset pricing finance. Our approach builds directly on recently developed realized variation measures and non-parametric jump detection statistics constructed from high-frequency intra-day data. A sequence of simple-to-implement moment-based tests involving various transformations of the daily returns speak directly to the importance of different distributional features, and may serve as useful diagnostic tools in the specification of empirically more realistic continuous-time asset pricing models. On applying the tests to the 30 individual stocks in the Dow Jones Industrial Average index, we find that it is important to allow for both time-varying diffusive volatility, jumps, and leverage effects to satisfactorily describe the daily stock price dynamics.

Testing for jumps in conditionally Gaussian ARMA–GARCH models, a robust approach

“…The model for r * t , resulting from (2.1)-(2.4), is a combination of an approximation of a smooth and slowly reverting continuous sample path process and a much less persistent jump component, that according to Andersen, Bollerslev, Frederiksen, and Nielsen (2010) best describes many (log-)return processes. It is also an approximation of the decomposition of asset returns sampled at high frequency into their base components (continuous, small jumps, large jumps)…”

“…They also find that conditional covariance forecasts obtained from various multivariate models, including the DCC model, are frequently outperformed by their jump-robust version based on ex post realized covariance estimates from high-frequency EUR-USD and YEN-USD exchange rates over the period 2004-2009. on bipower variation, an important segment of the literature uses realized moments from high frequency data to estimate the jump component by substracting realized bipower variation from realized volatility and to provide non-parametric jump detection statistics for testing its significance at a lower observation frequency (see e.g. Andersen, Bollerslev, Frederiksen, and Nielsen, 2010). Multipower extensions have been considered by Barndorff-Nielsen and Shephard (2006) and Huang and Tauchen (2006).…”

Time Change, Volatility, and Turbulence

“…At least as a first approximation this is close to reality, see for instance [ABDE01]. Recent, more refined, empirical analysis takes the possibilities of jumps and of microstructure noise, which are not covered by (23), into account; see [ABFN06].…”

The Dual Micro/Macro Informing Role of Social Network Sites: Can Twitter Macro Messages Help Predict Stock Prices?

“…To achieve the first goal, many methods of forecasting stock prices are used in research and practice, ranging from human "black box" expertise (Soderlind, 2010) to soft computing techniques that number in the hundreds of methods (Atsalakis & Valavanis, 2009). Time series analysis is often a part of these methods and is applied in order to identify trends and analyze patterns (Andersen, Bollerslev, Frederiksen, & Nielsen, 2010;Hwang & Oh, 2010). Recent studies of note include a time-series forecasting solution using the dividend-price ratio, earnings growth, and price-earnings ratio growth in a sum-of-the-parts method, which yielded better Rsquares than standard predictive regressions (Ferreira & Santa-Clara, 2011), and a study on the causal impact of media in financial markets which found that earnings announcements in local media coverage strongly predicted local trading for S&P 500 firms (Engelberg & Parsons, 2011).…”