Volatility Forecasting

Abstract

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management.Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly.

Testing Models of Low-Frequency Variability

“…However, instability in the second moment of financial and macroeconomic data is often quite persistent (e.g., Bollerslev, Engle, and Nelson (1994) and Andersen, Bollerslev, Christoffersen, and Diebold (2007), Balke and Gordon (1989), Kim and Nelson (1999), and McConnell and Perez-Quiros (2000)), so it is interesting to ask whether second moments of u t exhibit enough low-frequency variability to invalidate limits like those shown in Table I. To investigate this, we nest each of the models considered thus far in a more general model that allows for such low-frequency heteroskedasticity, derive the resulting value of Σ for the more general model, and construct an optimal test against such alternatives.…”

A high–low model of daily stock price ranges

“…Volatility forecasting is an active research area and has significant implications for financial market practitioners. Andersen et al (2005) and Poon and Granger (2003) are two recent extensive surveys on the subject. 12 Strictly speaking, the volatility of a stock index is an unobservable parameter that determines the index's observed variations.…”

Heterogeneous Gain Learning and the Dynamics of Asset Prices

“…18 See Bollerslev, Engle & Nelson (1995) or Andersen, Bollerslev, Christoffersen & Diebold (2005) for surveys of the large literature on volatility modeling.…”