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on Forecasting |
| By: | Torben G. Andersen (Department of Finance, Kellogg School of Management, Northwestern University, Evanston, IL 60208, and NBER); Tim Bollerslev (Department of Economics, Duke University, Durham, NC 27708, and NBER); Peter F. Christoffersen (Faculty of Management, McGill University, Montreal, Quebec, H3A 1G5, and CIRANO); Francis X. Diebold (Department of Economics, University of Pennsylvania, Philadelphia, PA 19104, and NBER) |
| 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. |
| JEL: | C10 C53 G1 |
| Date: | 2005–01–08 |
| URL: | http://d.repec.org/n?u=RePEc:cfs:cfswop:wp200508&r=for |
| By: | Francis X. Diebold (University of Pennsylvania, and NBER); Canlin Li (University of California) |
| Abstract: | Despite powerful advances in yield curve modeling in the last twenty years, comparatively little attention has been paid to the key practical problem of forecasting the yield curve. In this paper we do so. We use neither the no-arbitrage approach, which focuses on accurately fitting the cross section of interest rates at any given time but neglects time-series dynamics, nor the equilibrium approach, which focuses on time-series dynamics (primarily those of the instantaneous rate) but pays comparatively little attention to fitting the entire cross section at any given time and has been shown to forecast poorly. Instead, we use variations on the Nelson-Siegel exponential components framework to model the entire yield curve, period-by-period, as a three-dimensional parameter evolving dynamically. We show that the three time-varying parameters may be interpreted as factors corresponding to level, slope and curvature, and that they may be estimated with high efficiency. We propose and estimate autoregressive models for the factors, and we show that our models are consistent with a variety of stylized facts regarding the yield curve. We use our models to produce term-structure forecasts at both short and long horizons, with encouraging results. In particular, our forecasts appear much more accurate at long horizons than various standard benchmark forecasts. |
| Keywords: | Term structure, yield curve, factor model, Nelson-Siegel curve |
| JEL: | G1 E4 C5 |
| Date: | 2004–01–09 |
| URL: | http://d.repec.org/n?u=RePEc:cfs:cfswop:wp200409&r=for |
| By: | Peter F. Christoffersen (McGill University and CIRANO); Francis X. Diebold (University of Pennsylvania and NBER) |
| Abstract: | We consider three sets of phenomena that feature prominently – and separately – in the financial economics literature: conditional mean dependence (or lack thereof) in asset returns, dependence (and hence forecastability) in asset return signs, and dependence (and hence forecastability) in asset return volatilities. We show that they are very much interrelated, and we explore the relationships in detail. Among other things, we show that: (a) Volatility dependence produces sign dependence, so long as expected returns are nonzero, so that one should expect sign dependence, given the overwhelming evidence of volatility dependence; (b) The standard finding of little or no conditional mean dependence is entirely consistent with a significant degree of sign dependence and volatility dependence; (c) Sign dependence is not likely to be found via analysis of sign autocorrelations, runs tests, or traditional market timing tests, because of the special nonlinear nature of sign dependence; (d) Sign dependence is not likely to be found in very high-frequency (e.g., daily) or very low-frequency (e.g., annual) returns; instead, it is more likely to be found at intermediate return horizons; (e) Sign dependence is very much present in actual U.S. equity returns, and its properties match closely our theoretical predictions; (f) The link between volatility forecastability and sign forecastability remains intact in conditionally non-Gaussian environments, as for example with time-varying conditional skewness and/or kurtosis. |
| Date: | 2004–01–08 |
| URL: | http://d.repec.org/n?u=RePEc:cfs:cfswop:wp200408&r=for |
| By: | Sean D. Campbell (Brown University); Francis X. Diebold (University of Pennsylvania, and NBER) |
| Abstract: | We take a simple time-series approach to modeling and forecasting daily average temperature in U.S. cities, and we inquire systematically as to whether it may prove useful from the vantage point of participants in the weather derivatives market. The answer is, perhaps surprisingly, yes. Time-series modeling reveals conditional mean dynamics, and crucially, strong conditional variance dynamics, in daily average temperature, and it reveals sharp differences between the distribution of temperature and the distribution of temperature surprises. As we argue, it also holds promise for producing the long-horizon predictive densities crucial for pricing weather derivatives, so that additional inquiry into time-series weather forecasting methods will likely prove useful in weather derivatives contexts. |
| Keywords: | Risk management; hedging; insurance; seasonality; temperature; financial derivatives |
| Date: | 2004–01–10 |
| URL: | http://d.repec.org/n?u=RePEc:cfs:cfswop:wp200410&r=for |
| By: | Markus Haas (University of Munich); Stefan Mittnik (University of Munich); Bruce Mizrach (Rutgers University) |
| Abstract: | Financial markets embed expectations of central bank policy into asset prices. This paper compares two approaches that extract a probability density of market beliefs. The first is a simulatedmoments estimator for option volatilities described in Mizrach (2002); the second is a new approach developed by Haas, Mittnik and Paolella (2004a) for fat-tailed conditionally heteroskedastic time series. In an application to the 1992-93 European Exchange Rate Mechanism crises, that both the options and the underlying exchange rates provide useful information for policy makers. |
| Keywords: | Options; Implied Probability Densities; GARCH; Fat-tails; Exchange Rate Mechanism |
| JEL: | G12 G14 F31 |
| Date: | 2005–01–09 |
| URL: | http://d.repec.org/n?u=RePEc:cfs:cfswop:wp200509&r=for |
| By: | Sydney C. Ludvigson; Serena Ng |
| Abstract: | A key criticism of the existing empirical literature on the risk-return relation relates to the relatively small amount of conditioning information used to model the conditional mean and conditional volatility of excess stock market returns. To the extent that financial market participants have information not reflected in the chosen conditioning variables, measures of conditional mean and conditional volatility--and ultimately the risk-return relation itself--will be misspecified and possibly highly misleading. We consider one remedy to these problems using the methodology of dynamic factor analysis for large datasets, whereby a large amount of economic information can be summarized by a few estimated factors. We find that three new factors, a "volatility," "risk premium," and "real" factor, contain important information about one-quarter ahead excess returns and volatility that is not contained in commonly used predictor variables. Moreover, the factor-augmented specifications we examine predict an unusual 16-20 percent of the one-quarter ahead variation in excess stock market returns, and exhibit remarkably stable and strongly statistically significant out-of-sample forecasting power. Finally, in contrast to several pre-existing studies that rely on a small number of conditioning variables, we find a positive conditional correlation between risk and return that is strongly statistically significant, whereas the unconditional correlation is weakly negative and statistically insignificant. |
| JEL: | G12 G10 |
| Date: | 2005–07 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:11477&r=for |
| By: | Junsoo Lee; John A. List; Mark Strazicich |
| Abstract: | In this paper we examine temporal properties of eleven natural resource real price series from 1870-1990 by employing a Lagrangian Multiplier unit root test that allows for two endogenously determined structural breaks with and without a quadratic trend. Contrary to previous research, we find evidence against the unit root hypothesis for all price series. Our findings support characterizing natural resource prices as stationary around deterministic trends with structural breaks. This result is important in both a positive and normative sense. For example, without an appropriate understanding of the dynamics of a time series, empirical verification of theories, forecasting, and proper inference are potentially fruitless. More generally, we show that both pre-testing for unit roots with breaks and allowing for breaks in the forecast model can improve forecast accuracy. |
| JEL: | Q31 C12 C53 |
| Date: | 2005–07 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:11487&r=for |