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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 84 (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)
Cointegration and LongHorizon Forecasting
 Journal of Business and Economic Statistics
, 1997
"... : We consider the forecasting of cointegrated variables, and we show that at long horizons nothing is lost by ignoring cointegration when forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate BoxJenkins forecasts are just as accurate. Our results ..."
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Cited by 29 (1 self)
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: We consider the forecasting of cointegrated variables, and we show that at long horizons nothing is lost by ignoring cointegration when forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate BoxJenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measuresthey fail to value the maintenance of cointegrating relationships among variables and we suggest alternatives that explicitly do so. KEY WORDS: Prediction, Loss Function, Integration, Unit Root  2  1. INTRODUCTION Cointegration implies restrictions on the lowfrequency dynamic behavior of multivariate time series. Thus, imposition of cointegrating restrictions has immediate implications for the behavior of longhorizon forecasts, and it is widely believed that imposition of cointegrating restrictions, when they are in fact true, will produce superior longhorizon forecasts. Stock (1995, p. 1), for ...
Why are BeveridgeNelson and UnobservedComponent
 Decompositions of GDP So Different?, Review of Economics and Statistics, forthcoming
, 2002
"... 1 The decomposition of real GDP into trend and cycle remains a problem of considerable practical importance, but two widely used methods yield starkly different results. The unobserved component approach, introduced by Harvey (1985) and Clark (1987), implies a very smooth trend with a cycle that is ..."
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Cited by 25 (8 self)
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1 The decomposition of real GDP into trend and cycle remains a problem of considerable practical importance, but two widely used methods yield starkly different results. The unobserved component approach, introduced by Harvey (1985) and Clark (1987), implies a very smooth trend with a cycle that is large in amplitude and highly persistent. In contrast, the approach of Beveridge and Nelson (1981) implies that much of the variation in the series is attributable to variation in the trend while the cycle component is small and noisy. This conflict is apparent in Figures 1 and 2 in this paper where the two cycle components are plotted, and has been widely noted; see Watson (1986) Stock and Watson (1988) among others. It should surprise us that the unobserved component (UC) and BeveridgeNelson (BN) methods produce very different trendcycle decompositions since both are modelbased. Each implies an ARIMA representation. Neither imposes smoothness in the trend component a priori as does the smoother of Hodrick and Prescott (1997) or as in the polar case of a linear trend that forces all variation, save constant growth, into the cycle. The UC and BN both "let the data speak for itself " in this regard. While it is often stated
2007a, Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity
 Journal of Econometrics
"... Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing varia ..."
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Cited by 22 (6 self)
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Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. We establish instead that a suitable transformation of the forecast error known as the generalized forecast error possesses an equivalent set of properties. The paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts.
A Parallel CuttingPlane Algorithm for the Vehicle Routing Problem With Time Windows
, 1999
"... In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may on ..."
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Cited by 11 (1 self)
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In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may only serve the customers on a route if the total demand does not exceed the capacity of the vehicle. The most effective solution method proposed to date for this problem is due to Kohl, Desrosiers, Madsen, Solomon, and Soumis. Their algorithm uses a cuttingplane approach followed by a branchand bound search with column generation, where the columns of the LP relaxation represent routes of individual vehicles. We describe a new implementation of their method, using Karger's randomized minimumcut algorithm to generate cutting planes. The standard benchmark in this area is a set of 87 problem instances generated in 1984 by M. Solomon; making using of parallel processing in both the cuttingpla...
Structural time series models with common trends and common cycles
, 2003
"... This paper models and estimates the BeveridgeNelson decomposition of multivariate time series in an unobserved components framework. This is an alternative to standard approaches based on VAR and VECM models. The appeal of this method lies in its transparency and structural character. The basic mod ..."
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Cited by 6 (1 self)
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This paper models and estimates the BeveridgeNelson decomposition of multivariate time series in an unobserved components framework. This is an alternative to standard approaches based on VAR and VECM models. The appeal of this method lies in its transparency and structural character. The basic model parsimoniously nests a large set of common trend and common cycle restrictions. It is found that if the cyclical component has a sufficiently rich serial correlation pattern, all covariance terms of the trend and cycle innovations are identified. Tests for common trends are based on a method developed by Nyblom and Harvey (2000), while hypotheses on common cycles are tested using likelihood ratio statistics with standard distributions. This testing framework is used to assess the implications of common trendcommon cycle restrictions for the incomeconsumption relationship in U.S. data. The presence of a common cyclical component yields a rejection of the permanent income hypothesis and evidence is found for the stylized fact that permanent shocks play a more important role for consumption than for income. Outofsample forecasts show that common trend and common cycle restrictions improve predictive accuracy.
The Taylor Rule: A Spurious Regression? ♣
, 2003
"... This paper investigates the econometric properties of the Taylor (1993) rule applied to U.S., Australian and Swedish data to judge its empirical relevance. Little attention has been paid to the time series properties of the data underlying interest rate rules, nor the estimations themselves, despite ..."
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Cited by 5 (0 self)
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This paper investigates the econometric properties of the Taylor (1993) rule applied to U.S., Australian and Swedish data to judge its empirical relevance. Little attention has been paid to the time series properties of the data underlying interest rate rules, nor the estimations themselves, despite the rise in popularity of Taylorlike rules in both empirical and theoretical work. Unit root tests indicate that the variables commonly used in such modelling are likely to be integrated of order one or near integrated. Given that the variables in the Taylor rule are integrated of order one or near integrated processes, cointegration is a necessary condition both for consistent estimation of the parameters of the model and compatibility between the model and the data. Tests find little support for cointegration and, together with an outofsample forecast exercise, suggest that we should have serious doubts about the Taylor rule as a reasonable description of how monetary policy is conducted in the countries considered in this study. Parameter estimates from the standard Taylor rule regressions are therefore likely to be inconsistent and caution should be taken before for central bank policy is evaluated using such methods. JEL Classification: E52
Measuring lag structure in forecasting models  the introduction of Time Distance
, 1999
"... In modeling series with leading or lagging indicators, it is desirable to begin comparing models in terms of time distance. This paper formalizes the concept of time distance in terms of various metrics, and investigates the behaviors of these metrics. It is shown that under some circumstances, ti ..."
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Cited by 4 (1 self)
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In modeling series with leading or lagging indicators, it is desirable to begin comparing models in terms of time distance. This paper formalizes the concept of time distance in terms of various metrics, and investigates the behaviors of these metrics. It is shown that under some circumstances, time distance metrics indeed perform better in forecasting than standard measures (such as mean squared forecasting errors), and that some timedistance metrics outperform others. Department of Economics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 920930508, USA, email:cgranger@ucsd.edu. This researchwas partially funded by NSF grant SBR9708615. y Center for Basic Research in the Social Sciences, Harvard University, 34 Kirkland Street, Cambridge, MA 02138,USA, email:yjeon@latte.harvard.edu. 1 1 Introduction If one has a pair of time series, x t and y t , their "nearness" is usually measured in terms of their vertical difference z t = x t ; y t , using the abso...
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 3 (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
The Impact of Demography on the Real Exchange Rate
, 2001
"... Theory predicts that life cycle saving mechanisms will cause real exchange rate variations as the age structure varies. We investigate the impact of demography on the Swedish real exchange rate, measured as the real TCW index, during 1960 to 2000. Time series regressions show that the Swedish demogr ..."
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Cited by 2 (0 self)
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Theory predicts that life cycle saving mechanisms will cause real exchange rate variations as the age structure varies. We investigate the impact of demography on the Swedish real exchange rate, measured as the real TCW index, during 1960 to 2000. Time series regressions show that the Swedish demographic structure has significant explanatory power on the real exchange rate. A model using age shares alone as regressors is used for medium term outofsample forecasts, outperforming both a naive forecast and forecasts based on an autoregressive model. Finally we use the estimated model in order to make forecasts of the Swedish real exchange rate up to 2015. The model predicts that the Swedish age structure will have a depreciating effect on the real exchange rate up to 2007 followed by an appreciating effect in the end of the forecasting period.