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Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts
"... Volatility permeates modern financial theories and decision making processes. As such, accurate measures and good forecasts of future volatility are critical for the implementation and evaluation of asset and derivative pricing theories as well as trading and hedging strategies. In response to this, ..."
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Cited by 271 (33 self)
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Volatility permeates modern financial theories and decision making processes. As such, accurate measures and good forecasts of future volatility are critical for the implementation and evaluation of asset and derivative pricing theories as well as trading and hedging strategies. In response to this, a voluminous literature has emerged for modeling the temporal dependencies in financial market volatility at the daily and lower frequencies using ARCH and stochastic volatility type models. Most of these studies find highly significant insample parameter estimates and pronounced intertemporal volatility persistence. Meanwhile, when judged by standard forecast evaluation criteria, based on the squared or absolute returns over daily or longer forecast horizons, standard volatility models provide seemingly poor forecasts. The present paper demonstrates that, contrary to this contention, in empirically realistic situations the models actually produce strikingly accurate interdaily forecasts f...
Evaluating Interval Forecasts
 International Economic Review
, 1997
"... This paper is intended to address the deficiency by clearly defining what is meant by a "good" interval forecast, and describing how to test if a given interval forecast deserves the label "good". One of the motivations of Engle's (1982) classic paper was to form dynamic interval forecasts around po ..."
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Cited by 166 (10 self)
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This paper is intended to address the deficiency by clearly defining what is meant by a "good" interval forecast, and describing how to test if a given interval forecast deserves the label "good". One of the motivations of Engle's (1982) classic paper was to form dynamic interval forecasts around point predictions. The insight was that the intervals should be narrow in tranquil times and wide in volatile times, so that the occurrences of observations outside the interval forecast would be spread out over the sample and not come in clusters. An interval forecast that 3 fails to account for higherorder dynamics may be correct on average (have correct unconditional coverage), but in any given period it will have incorrect conditional coverage characterized by clustered outliers. These concepts will be defined precisely below, and tests for correct conditional coverage are suggested. Chatfield (1993) emphasizes that model misspecification is a much more important source of poor interval forecasting than is simple estimation error. Thus, our testing criterion and the tests of this criterion are model free. In this regard, the approach taken here is similar to the one taken by Diebold and Mariano (1995). This paper can also be seen as establishing a formal framework for the ideas suggested in Granger, White and Kamstra (1989). Recently, financial market participants have shown increasing interest in interval forecasts as measures of uncertainty. Thus, we apply our methods to the interval forecasts provided by J.P. Morgan (1995). Furthermore, the socalled "ValueatRisk" measures suggested for risk measurement correspond to tail forecasts, i.e., onesided interval forecasts of portfolio returns. Lopez (1996) evaluates these types of forecasts applying the procedures develo...
Consumption, Aggregate Wealth, and Expected Stock Returns
 THE JOURNAL OF FINANCE • VOL. LVI, NO. 3 • JUNE 2001
, 2001
"... This paper studies the role of fluctuations in the aggregate consumption–wealth ratio for predicting stock returns. Using U.S. quarterly stock market data, we find that these fluctuations in the consumption–wealth ratio are strong predictors of both real stock returns and excess returns over a Treas ..."
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Cited by 150 (18 self)
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This paper studies the role of fluctuations in the aggregate consumption–wealth ratio for predicting stock returns. Using U.S. quarterly stock market data, we find that these fluctuations in the consumption–wealth ratio are strong predictors of both real stock returns and excess returns over a Treasury bill rate. We also find that this variable is a better forecaster of future returns at short and intermediate horizons than is the dividend yield, the dividend payout ratio, and several other popular forecasting variables. Why should the consumption–wealth ratio forecast asset returns? We show that a wide class of optimal models of consumer behavior imply that the log consumption–aggregate wealth ~human capital plus asset holdings! ratio summarizes expected returns on aggregate wealth, or the market portfolio. Although this ratio is not observable, we provide assumptions under which its important predictive components for future asset returns may be expressed in terms of observable variables, namely in terms of consumption, asset holdings and labor income. The framework implies that these variables are cointegrated, and
Strictly Proper Scoring Rules, Prediction, and Estimation
, 2007
"... Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F if he ..."
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Cited by 143 (17 self)
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Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F if he or she issues the probabilistic forecast F, rather than G ̸ = F. It is strictly proper if the maximum is unique. In prediction problems, proper scoring rules encourage the forecaster to make careful assessments and to be honest. In estimation problems, strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand. This article reviews and develops the theory of proper scoring rules on general probability spaces, and proposes and discusses examples thereof. Proper scoring rules derive from convex functions and relate to information measures, entropy functions, and Bregman divergences. In the case of categorical variables, we prove a rigorous version of the Savage representation. Examples of scoring rules for probabilistic forecasts in the form of predictive densities include the logarithmic, spherical, pseudospherical, and quadratic scores. The continuous ranked probability score applies to probabilistic forecasts that take the form of predictive cumulative distribution functions. It generalizes the absolute error and forms a special case of a new and very general type of score, the energy score. Like many other scoring rules, the energy score admits a kernel representation in terms of negative definite functions, with links to inequalities of Hoeffding type, in both univariate and multivariate settings. Proper scoring rules for quantile and interval forecasts are also discussed. We relate proper scoring rules to Bayes factors and to crossvalidation, and propose a novel form of crossvalidation known as randomfold crossvalidation. A case study on probabilistic weather forecasts in the North American Pacific Northwest illustrates the importance of propriety. We note optimum score approaches to point and quantile
Forecasting the term structure of government bond yields
 Journal of Econometrics
, 2006
"... 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 noarbitrage approach, which focuses on accurately fitting the cross sectio ..."
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Cited by 134 (12 self)
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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 noarbitrage approach, which focuses on accurately fitting the cross section of interest rates at any given time but neglects timeseries dynamics, nor the equilibrium approach, which focuses on timeseries 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 NelsonSiegel exponential components framework to model the entire yield curve, periodbyperiod, as a threedimensional parameter evolving dynamically. We show that the three timevarying 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 termstructure 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. Finally, we discuss a number of extensions, including generalized duration measures, applications to active bond portfolio management, and arbitragefree specifications. Acknowledgments: The National Science Foundation and the Wharton Financial Institutions Center provided research support. For helpful comments we are grateful to Dave Backus, Rob Bliss, Michael Brandt, Todd Clark, Qiang Dai, Ron Gallant, Mike Gibbons, Da...
A Comprehensive Look at the Empirical Performance of Equity Premium Prediction,” working paper
, 2004
"... Given the historically high equity premium, is it now a good time to invest in the stock market? Economists have suggested a whole range of variables that investors could or should use to predict: dividend price ratios, dividend yields, earningsprice ratios, dividend payout ratios, net issuing rati ..."
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Cited by 125 (4 self)
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Given the historically high equity premium, is it now a good time to invest in the stock market? Economists have suggested a whole range of variables that investors could or should use to predict: dividend price ratios, dividend yields, earningsprice ratios, dividend payout ratios, net issuing ratios, bookmarket ratios, interest rates (in various guises), and consumptionbased macroeconomic ratios (cay). The typical paper reports that the variable predicted well in an insample regression, implying forecasting ability. Our paper explores the outofsample performance of these variables, and finds that not a single one would have helped a realworld investor outpredicting the thenprevailing historical equity premium mean. Most would have outright hurt. Therefore, we find that, for all practical purposes, the equity premium has not been predictable, and any belief about whether the stock market is now too high or too low has to be based on theoretical prior, not on the empirically variables we have explored.
What does the Yield Curve Tell us about GDP Growth?
, 2003
"... A lot, including a few things you may not expect. Previous studies find that the term spread forecasts GDP but these regressions are unconstrained and do not model regressor endogeneity. We build a dynamic model for GDP growth and yields that completely characterizes expectations of GDP. The model d ..."
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Cited by 101 (4 self)
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A lot, including a few things you may not expect. Previous studies find that the term spread forecasts GDP but these regressions are unconstrained and do not model regressor endogeneity. We build a dynamic model for GDP growth and yields that completely characterizes expectations of GDP. The model does not permit arbitrage. Contrary to previous findings, we predict that the short rate has more predictive power than any term spread. We confirm this finding by forecasting GDP outofsample. The model also recommends the use of lagged GDP and the longest maturity yield to measure slope. Greater efficiency enables the yieldcurve model to produce superior outofsample GDP forecasts than unconstrained OLS at all horizons.
2006) Approximately normal tests for equal predictive accuracy in nested models. Journal of Econometrics forthcoming
"... Forecast evaluation often compares a parsimonious null model to a larger model that nests the null model. Under the null that the parsimonious model generates the data, the larger model introduces noise into its forecasts by estimating parameters whose population values are zero. We observe that the ..."
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Cited by 86 (13 self)
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Forecast evaluation often compares a parsimonious null model to a larger model that nests the null model. Under the null that the parsimonious model generates the data, the larger model introduces noise into its forecasts by estimating parameters whose population values are zero. We observe that the mean squared prediction error (MSPE) from the parsimonious model is therefore expected to be smaller than that of the larger model. We describe how to adjust MSPEs to account for this noise. We propose applying standard methods (West (1996)) to test whether the adjusted mean squared error difference is zero. We refer to nonstandard limiting distributions derived in Clark and McCracken (2001, 2005a) to argue that use of standard normal critical values will yield actual sizes close to, but a little less than, nominal size. Simulation evidence supports our recommended procedure. West thanks the National Science Foundation for financial support. We thank Pablo M. PincheiraBrown and Taisuke Nakata for helpful comments. The views expressed herein are solely those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System.
Forecast Evaluation and Combination
 IN G.S. MADDALA AND C.R. RAO (EDS.), HANDBOOK OF STATISTICS
, 1996
"... It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately forecast users naturally have a keen interest in monitoring and ..."
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Cited by 85 (24 self)
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It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately forecast users naturally have a keen interest in monitoring and improving forecast performance. More generally, forecast evaluation figures prominently in many questions in empirical economics and finance, such as: Are expectations rational? (e.g., Keane and Runkle, 1990; Bonham and Cohen, 1995) Are financial markets efficient? (e.g., Fama, 1970, 1991) Do macroeconomic shocks cause agents to revise their forecasts at all horizons, or just at short and mediumterm horizons? (e.g., Campbell and Mankiw, 1987; Cochrane, 1988) Are observed asset returns "too volatile"? (e.g., Shiller, 1979; LeRoy and Porter, 1981) Are asset returns forecastable over long horizons? (e.g., Fama and French, 1988; Mark, 1995)