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Volatility Forecast Comparison Using Imperfect Volatility Proxies
 JOURNAL OF ECONOMETRICS
, 2010
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Comparing Density Forecasts Using Threshold and Quantile Weighted Scoring Rules
, 2008
"... We propose a method for comparing density forecasts that is based on weighted versions of the continuous ranked probability score. The weighting emphasizes regions of interest, such as the tails or the center of a variable’s range, while retaining propriety, as opposed to a recently developed weight ..."
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Cited by 20 (1 self)
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We propose a method for comparing density forecasts that is based on weighted versions of the continuous ranked probability score. The weighting emphasizes regions of interest, such as the tails or the center of a variable’s range, while retaining propriety, as opposed to a recently developed weighted likelihood ratio test, which can be hedged. Threshold and quantile based decompositions of the continuous ranked probability score can be illustrated graphically and prompt insights into the strengths and deficiencies of a forecasting method. We illustrate the use of the test and graphical tools in case studies on the Bank of England’s density forecasts of quarterly inflation rates in the United Kingdom, and probabilistic predictions of wind resources in the
Consistent ranking of multivariate volatility models
"... A large number of parameterizations have been proposed to model conditional variance dynamics in a multivariate framework. This paper examines the ranking of multivariate volatility models in terms of their ability to forecast outofsample conditional variance matrices. We investigate how sensitive ..."
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Cited by 18 (0 self)
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A large number of parameterizations have been proposed to model conditional variance dynamics in a multivariate framework. This paper examines the ranking of multivariate volatility models in terms of their ability to forecast outofsample conditional variance matrices. We investigate how sensitive the ranking is to alternative statistical loss functions which evaluate the distance between the true covariance matrix and its forecast. The evaluation of multivariate volatility models requires the use of a proxy for the unobservable volatility matrix which may shift the ranking of the models. Therefore, to preserve this ranking conditions with respect to the choice of the loss function have to be discussed. To do this, we extend the conditions defined in Hansen and Lunde (2006) to the multivariate framework. By invoking norm equivalence we are able to extend the class of loss functions that preserve the true ranking. In a simulation study, we sample data from a continuous time multivariate diffusion process to illustrate the sensitivity of the ranking to different choices of the loss functions and to the quality of the proxy. An application to three foreign exchange rates, where we compare the forecasting performance of 16 multivariate GARCH
Inflation Dynamics and Food Prices in an Agricultural Economy: The Case of Ethiopia. Policy Research Working Paper 4969, The World Bank, Africa Region, Agricultural and Rural Development Unit
, 2009
"... Ethiopia has experienced a historically unprecedented increase in inflation, mainly driven by cereal price inflation, which is among the highest in SubSaharan Africa. Using monthly data over the past decade, we estimate error correction models to identify the relative importance of several factors ..."
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Cited by 12 (1 self)
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Ethiopia has experienced a historically unprecedented increase in inflation, mainly driven by cereal price inflation, which is among the highest in SubSaharan Africa. Using monthly data over the past decade, we estimate error correction models to identify the relative importance of several factors contributing to overall inflation and its three major components, cereal prices, food prices and nonfood prices. Our main finding is that, in a longer perspective, over three to four years, domestic food and nonfood prices are determined by the exchange rate and international food and goods prices. In the short run, agricultural supply shocks and inflation inertia strongly affect domestic inflation, causing large deviations from longrun price trends. Money supply growth does affect food price inflation in the short run, though the money stock itself does not seem to drive inflation. Our results suggest the need for a multipronged approach to fight inflation. Forecast scenarios suggest monetary and exchange rate policies need to take into account cereal production, which is among the key determinants of inflation, assuming a decline in global commodity prices. Implementation of successful policies will be contingent on the availability of foreign exchange and the performance of agriculture.
On loss functions and ranking forecasting performances of multivariate volatility models. Working paper
, 2009
"... A large number of parameterizations have been proposed to model conditional variance dynamics in a multivariate framework. However, little is known about the ranking of multivariate volatility models in terms of their forecasting ability. The ranking of multivariate volatility models is inherently ..."
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Cited by 10 (2 self)
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A large number of parameterizations have been proposed to model conditional variance dynamics in a multivariate framework. However, little is known about the ranking of multivariate volatility models in terms of their forecasting ability. The ranking of multivariate volatility models is inherently problematic because when the unobservable volatility is substituted by a proxy, the ordering implied by a loss function may result to be biased with respect to the intended one. We point out that the size of the distortion is strictly tied to the level of the accuracy of the volatility proxy. We propose a generalized necessary and sufficient functional form for a class of nonmetric distance measures of the Bregman type, suited to vector and matrix spaces, which ensure consistency of the ordering when the target is observed with noise. An application to three foreign exchange rates, where we compare the forecasting performance of 24 multivariate GARCH specifi
2009, Multiperiod forecasts of volatility: Direct, iterated, and mixeddata approaches, Discussion Paper
"... Multiperiod forecasts of stock market return volatilities are often used in asset pricing, portfolio allocation, riskmanagement and most other areas of finance where longhorizon measures of risk are necessary. Yet, very little is known about how to forecast volatility several periods ahead, as mos ..."
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Cited by 8 (2 self)
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Multiperiod forecasts of stock market return volatilities are often used in asset pricing, portfolio allocation, riskmanagement and most other areas of finance where longhorizon measures of risk are necessary. Yet, very little is known about how to forecast volatility several periods ahead, as most of the focus has been on oneperiodahead forecasts. In this paper, we compare several approaches of producing multiperiod ahead forecasts of volatility – iterated, direct, and mixeddata sampling (MIDAS) – as alternatives to the oftenused “scaling ” method. The comparison is conducted (pseudo) outofsample using returns data of the US stock market portfolio and a cross section of size, booktomarket, and industry portfolios. The results are surprisingly sharp. For the market and all other portfolios, we obtain the same ordering of the volatility forecasting methods. The direct approach provides the worse (in MSFE sense) forecasts; it is dominated even by the naive scaling method. Iterated forecasts are suitable for shorter horizons (5 to 10 days ahead), but their MSFEs deteriorate rapidly as the horizon increases. The MIDAS forecasts perform well at long horizons:
Combining Probability Forecasts
, 2008
"... Linear pooling is by the far the most popular method for combining probability forecasts. However, any nontrivial weighted average of two or more distinct, calibrated probability forecasts is necessarily uncalibrated and lacks sharpness. In view of this, linear pooling requires recalibration, even i ..."
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Cited by 7 (0 self)
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Linear pooling is by the far the most popular method for combining probability forecasts. However, any nontrivial weighted average of two or more distinct, calibrated probability forecasts is necessarily uncalibrated and lacks sharpness. In view of this, linear pooling requires recalibration, even in the ideal case in which the individual forecasts are calibrated. Toward this end, we propose a beta transformed linear opinion pool (BLP) for the aggregation of probability forecasts from distinct, calibrated or uncalibrated sources. The BLP method fits an optimal nonlinearly recalibrated forecast combination, by compositing a beta transform and the traditional linear opinion pool. The technique is illustrated in a simulation example and in a case study on statistical and National Weather Service probability of precipitation forecasts.
Understanding Models’ Forecasting Performance
 Journal of Econometrics
, 2011
"... We propose a new methodology to identify the sources of models ’ forecasting performance. The methodology decomposes the models ’ forecasting performance into asymptotically uncorrelated components that measure instabilities in the forecasting performance, predictive content, and overfitting. The ..."
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Cited by 5 (4 self)
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We propose a new methodology to identify the sources of models ’ forecasting performance. The methodology decomposes the models ’ forecasting performance into asymptotically uncorrelated components that measure instabilities in the forecasting performance, predictive content, and overfitting. The empirical application shows the usefulness of the new methodology for understanding the causes of the poor forecasting ability of economic models for exchange rate determination.
Quantiles as optimal point predictors
"... The loss function plays a central role in the theory and practice of forecasting. If the loss is quadratic, the mean of the predictive distribution is the unique optimal point predictor. If the loss is linear, any median is an optimal point forecast. The title of the paper refers to the simple, poss ..."
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Cited by 5 (2 self)
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The loss function plays a central role in the theory and practice of forecasting. If the loss is quadratic, the mean of the predictive distribution is the unique optimal point predictor. If the loss is linear, any median is an optimal point forecast. The title of the paper refers to the simple, possibly surprising fact that quantiles arise as optimal point predictors under a general class of economically relevant loss functions, to which we refer as generalized piecewise linear (GPL). The level of the quantile depends on a generic asymmetry parameter that reflects the possibly distinct costs of underprediction and overprediction. A loss function for which quantiles are optimal point predictors is necessarily GPL, similarly to the classical fact that a loss function for which the mean is optimal is necessarily of the Bregman type. We prove general versions of these results that apply on any decisionobservation domain and rest on weak assumptions. The empirical relevance of the choices in the transition from the predictive distribution to the point forecast is illustrated on the Bank of England’s density forecasts of United Kingdom inflation rates, and probabilistic predictions of wind energy resources in the Pacific Northwest. Key words and phrases: asymmetric loss function; Bayes predictor; density forecast; mean; median; mode; optimal point predictor; quantile; statistical decision theory 1
What do we Know about G7 Macro Forecasts
, 2008
"... Research Program on Forecasting (RPF) Working Papers represent preliminary work circulated for comment and discussion. Please contact the author(s) before citing this paper in any publications. The views expressed in RPF Working Papers are solely those of the author(s) and do not necessarily represe ..."
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Cited by 4 (2 self)
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Research Program on Forecasting (RPF) Working Papers represent preliminary work circulated for comment and discussion. Please contact the author(s) before citing this paper in any publications. The views expressed in RPF Working Papers are solely those of the author(s) and do not necessarily represent the views of RPF or George Washington University.