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31
Comparing Predictive Accuracy
 JOURNAL OF BUSINESS AND ECONOMIC STATISTICS, 13, 253265
, 1995
"... We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss function need not be quadratic, and need not even be symmetri ..."
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Cited by 901 (26 self)
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We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss function need not be quadratic, and need not even be symmetric), and forecast errors can be nonGaussian, nonzero mean, serially correlated, and contemporaneously correlated. Asymptotic and exact finite sample tests are proposed, evaluated, and illustrated.
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 122 (29 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 &quot;too volatile&quot;? (e.g., Shiller, 1979; LeRoy and Porter, 1981) Are asset returns forecastable over long horizons? (e.g., Fama and French, 1988; Mark, 1995)
On the OutofSample Importance of Skewness and Asymmetric Dependence for Asset Allocation
 Journal of Financial Econometrics
, 2004
"... Recent studies in the empirical finance literature have reported evidence of two types of asymmetries in the joint distribution of stock returns. The first is skewness in the distribution of individual stock returns. The second is an asymmetry in the dependence between stocks: stock returns appear t ..."
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Cited by 65 (3 self)
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Recent studies in the empirical finance literature have reported evidence of two types of asymmetries in the joint distribution of stock returns. The first is skewness in the distribution of individual stock returns. The second is an asymmetry in the dependence between stocks: stock returns appear to be more highly correlated during market downturns than during market upturns. In this article we examine the economic and statistical significance of these asymmetries for asset allocation decisions in an outofsample setting. We consider the problem of a constant relative risk aversion (CRRA) investor allocating wealth between the riskfree asset, a smallcap portfolio, and a largecap portfolio. We use models that can capture timevarying moments up to the fourth order, and we use copula theory to construct models of the timevarying dependence structure that allow for different dependence during bear markets than bull markets. The importance of these two asymmetries for asset allocation is assessed by comparing the performance of a portfolio based on a normal distribution model with a portfolio based on a more flexible distribution model. For investors with no shortsales constraints, we find that knowledge of higher moments and asymmetric dependence leads to gains that are economically significant and statistically significant in some cases. For short salesconstrained investors the gains are limited.
Economic forecasting
, 2007
"... Forecasts guide decisions in all areas of economics and finance and their value can only be understood in relation to, and in the context of, such decisions. We discuss the central role of the loss function in helping determine the forecaster’s objectives. Decision theory provides a framework for bo ..."
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Cited by 32 (1 self)
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Forecasts guide decisions in all areas of economics and finance and their value can only be understood in relation to, and in the context of, such decisions. We discuss the central role of the loss function in helping determine the forecaster’s objectives. Decision theory provides a framework for both the construction and evaluation of forecasts. This framework allows an understanding of the challenges that arise from the explosion in the sheer volume of predictor variables under consideration and the forecaster’s ability to entertain an endless array of forecasting models and timevarying specifications, none of which may coincide with the ‘true’ model. We show this along with reviewing methods for comparing the forecasting performance of pairs of models or evaluating the ability of the best of many models to beat a benchmark specification.
Predictive Ability with Cointegrated Variables
 Journal of Econometrics
, 2001
"... In this paper we outline conditions under which the Diebold and Mariano (DM: 1995) test for predictive ability can be extended to the case of two forecasting models, each of which may include cointegrating relations, when allowing for parameter estimation error. We show that in the cases where eithe ..."
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Cited by 23 (6 self)
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In this paper we outline conditions under which the Diebold and Mariano (DM: 1995) test for predictive ability can be extended to the case of two forecasting models, each of which may include cointegrating relations, when allowing for parameter estimation error. We show that in the cases where either the loss function is quadratic or the length of the prediction period, P, grows at a slower rate than the length of the regression period, R, the standard DM test can be used. On the other hand, in the case of a generic loss function, if P R ! as T ! 1, 0 < < 1, then the asymptotic normality result of West (1996) no longer holds. We also extend the "data snooping" technique of White (2000) for comparing the predictive ability of multiple forecasting models to the case of cointegrated variables. In a series of Monte Carlo experiments, we examine the impact of both short run and cointegrating vector parameter estimation error on DM, data snooping, and related tests. Our results sugge...
Nonparametric Bootstrap Procedures for Predictive Inference Based on Recursive Estimation Schemes
, 2005
"... We introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for outofsample n ..."
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Cited by 19 (6 self)
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We introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for outofsample nonlinear Granger causality, and in the other we outline a test for selecting amongst multiple alternative forecasting models, all of which are possibly misspecified. In a Monte Carlo investigation, we compare the finite sample properties of our block bootstrap procedures with the parametric bootstrap due to Kilian (1999); within the context of encompassing and predictive accuracy tests. In the empirical illustration, it is found that unemployment has nonlinear marginal predictive content for inflation.
Decisionmetrics: a decisionbased approach to econometric modelling
 Journal of Econometrics
, 2007
"... In many applications it is necessary to use a simple and therefore highly misspecified econometric model as the basis for decisionmaking. We propose an approach to developing a possibly misspecified econometric model that will be used as the beliefs of an objective expected utility maximiser. A dis ..."
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Cited by 16 (0 self)
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In many applications it is necessary to use a simple and therefore highly misspecified econometric model as the basis for decisionmaking. We propose an approach to developing a possibly misspecified econometric model that will be used as the beliefs of an objective expected utility maximiser. A discrepancy between model and ‘truth ’ is introduced that is interpretable as a measure of the model’s value for this decisionmaker. Our decisionbased approach utilises this discrepancy in estimation, selection, inference and evaluation of parametric or semiparametric models. The methods proposed nest quasilikelihood methods as a special case that arises when model value is measured by the KullbackLeibler information discrepancy and also provide an econometric approach for developing parametric decision rules (e.g. technical trading rules) with desirable properties. The approach is illustrated and applied in the context of a CARA investor’s decision problem for which analytical, simulation and empirical results suggest it is very effective.
An Out of Sample Test for Granger Causality
 Macroeconomic Dynamics
, 2000
"... Granger (1980) summarizes his personal viewpoint on testing for causality, and outlines what he considers to be a useful operational version of his original denition of causality (Granger (1969)), which he notes was partially alluded to in Wiener (1958). This operational version is based on a compar ..."
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Cited by 16 (5 self)
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Granger (1980) summarizes his personal viewpoint on testing for causality, and outlines what he considers to be a useful operational version of his original denition of causality (Granger (1969)), which he notes was partially alluded to in Wiener (1958). This operational version is based on a comparison of the 1step ahead predictive ability of competing models. However, Granger concludes his discussion by noting that it is common practice to test for Granger causality using insample Ftests. The practice of using insample type Granger causality tests continues to be prevalent. In this paper we develop simple (nonlinear) outofsample predictive ability tests of the Granger noncausality null hypothesis. In addition, Monte Carlo experiments are used to investigate the nite sample properites of the test. An empirical illustration shows that the choice of insample versus outofsample Granger causality tests can crucially aect the conclusions about the predictive content of money for ...
An Empirical Study of Seasonal Unit Roots in Forecasting
 International Journal of Forecasting
, 1997
"... We assess the usefulness of pretesting for seasonal roots, based on the HEGY approach, for outof sample forecasting. We show that if there are shifts in the deterministic seasonal components then the imposition of unit roots can partially robustify sequences of rolling forecasts, yielding improved ..."
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Cited by 11 (4 self)
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We assess the usefulness of pretesting for seasonal roots, based on the HEGY approach, for outof sample forecasting. We show that if there are shifts in the deterministic seasonal components then the imposition of unit roots can partially robustify sequences of rolling forecasts, yielding improved forecast accuracy. We illustrate with two empirical examples where more accurate forecasts can be obtained by imposing more roots than is warranted by HEGY. We address the issue of assessing forecast accuracy when predictions of any one of a number of linear transformations may be of interest. 1 Introduction An important strand of the recent literature on modelling seasonality in economic time series has been concerned with testing for seasonal unit roots. Hylleberg, Engle, Granger and Yoo (1990) (henceforth, HEGY) helped popularize the modelling of economic time series as variables which exhibit seasonal unit roots, but as those authors acknowledge, timeseries analysts in the tradition o...
Optimal Prediction Under Asymmetric Loss
, 1994
"... this paper we treat the prediction problem under general loss structures, building on the classic work of Granger (1969). In Section 2, we characterize the optimal predictor for nonGaussian processes under asymmetric loss. The results apply, for example, to important classes of conditionally heteros ..."
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Cited by 5 (1 self)
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this paper we treat the prediction problem under general loss structures, building on the classic work of Granger (1969). In Section 2, we characterize the optimal predictor for nonGaussian processes under asymmetric loss. The results apply, for example, to important classes of conditionally heteroskedastic processes. In Section 3, we provide analytic solutions for the optimal predictor under two popular analyticallytractable asymmetric loss functions. In Section 4, we provide methods for approximating the optimal predictor under more general loss functions. We conclude in Section 5. 2. OPTIMAL PREDICTION FOR NONGAUSSIAN PROCESSES Granger (1969) studies Gaussian processes and shows that under asymmetric loss the optimal predictor is the conditional mean plus a constant bias term. Granger's fundamental result, however, has two key limitations. First, the Gaussian assumption implies a constant L(y