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15
Probabilistic forecasts, calibration and sharpness
 Journal of the Royal Statistical Society Series B
, 2007
"... Summary. Probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive dis ..."
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Cited by 38 (15 self)
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Summary. Probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions. We propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive distributions subject to calibration. Calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize. Sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only. A simple theoretical framework allows us to distinguish between probabilistic calibration, exceedance calibration and marginal calibration. We propose and study tools for checking calibration and sharpness, among them the probability integral transform histogram, marginal calibration plots, the sharpness diagram and proper scoring rules. The diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the Stateline wind energy centre in the US Pacific Northwest. In combination with crossvalidation or in the time series context, our proposal provides very general, nonparametric alternatives to the use of information criteria for model diagnostics and model selection.
Geostatistical SpaceTime Models, Stationarity, Separability and Full Symmetry
"... Geostatistical approaches to modeling spatiotemporal data rely on parametric covariance models and rather stringent assumptions, such as stationarity, separability and full symmetry. This paper reviews recent advances in the literature on spacetime covariance functions in light of the aforemention ..."
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Cited by 15 (3 self)
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Geostatistical approaches to modeling spatiotemporal data rely on parametric covariance models and rather stringent assumptions, such as stationarity, separability and full symmetry. This paper reviews recent advances in the literature on spacetime covariance functions in light of the aforementioned notions, which are illustrated using wind data from Ireland. Experiments with timeforward kriging predictors suggest that the use of more complex and more realistic covariance models results in improved predictive performance.
Probabilistic Wind Speed Forecasting using Ensembles and Bayesian Model Averaging
, 2008
"... the Joint Ensemble Forecasting System (JEFS) under subcontract S0647225 from the University ..."
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Cited by 14 (8 self)
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the Joint Ensemble Forecasting System (JEFS) under subcontract S0647225 from the University
Powering up with spacetime wind forecasting
 Journal of the American Statistical Association
, 2009
"... The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. Highquality shortterm forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind spe ..."
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Cited by 6 (5 self)
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The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. Highquality shortterm forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information. The forecasts produced by this model are accurate, and subject to accuracy, the predictive distribution is sharp, i.e., highly concentrated around its center. However, this model is split into nonunique regimes based on the wind direction at an offsite location. This paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model. It is robust in many experiments, such as predicting at new locations. We compare this with the more common approach of modeling wind speeds and directions in the Cartesian space and use a skewt distribution for the errors. The quality of the predictions from all of these models can be more realistically assessed with a loss measure that depends upon the power curve relating wind speed to power output. This proposed loss measure yields more insight into the true value of each model’s predictions. Some key words: Circular variable, power curve, skewt distribution, wind direction, wind speed.
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 4 (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
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 3 (0 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
Probabilistic Forecasts of Wind Speed: Ensemble Model Output Statistics using Heteroskedastic Censored Regression
, 2008
"... As wind energy penetration continues to grow, there is a critical need for probabilistic forecasts of wind resources. In addition, there are many other societally relevant uses for forecasts of wind speed, ranging from aviation to ship routing and recreational boating. Over the past two decades, ens ..."
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Cited by 2 (1 self)
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As wind energy penetration continues to grow, there is a critical need for probabilistic forecasts of wind resources. In addition, there are many other societally relevant uses for forecasts of wind speed, ranging from aviation to ship routing and recreational boating. Over the past two decades, ensembles of numerical weather prediction (NWP) models have been developed, in which multiple estimates of the current state of the atmosphere are used to generate a collection of deterministic forecasts. However, even stateoftheart ensemble systems are uncalibrated and biased. Here we propose a novel way of statistically postprocessing NWP ensembles for wind speed using heteroskedastic censored (Tobit) regression, where location and spread derive from the ensemble forecast. The resulting ensemble model output statistics (EMOS) method is applied to 48hour ahead forecasts of maximum wind speed over the North American Pacific Northwest in 2003 using the University of Washington Mesoscale Ensemble. The statistically postprocessed EMOS density forecasts turn out to be calibrated and sharp, and result in substantial improvement over the unprocessed NWP ensemble or climatological reference forecasts.
Optimal Probabilistic Forecasts for Counts
, 2009
"... Optimal probabilistic forecasts of integervalued random variables are derived. The optimality is achieved by estimating the forecast distribution nonparametrically over a given broad model class and proving asymptotic efficiency in that setting. The ideas are demonstrated within the context of the ..."
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Cited by 2 (2 self)
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Optimal probabilistic forecasts of integervalued random variables are derived. The optimality is achieved by estimating the forecast distribution nonparametrically over a given broad model class and proving asymptotic efficiency in that setting. The ideas are demonstrated within the context of the integer autoregressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth and death process or branching process. The theoretical proofs of asymptotic optimality are supplemented by simulation results which demonstrate the overall superiority of the nonparametric method relative to a misspecified parametric maximum likelihood estimator, in large but finite samples. The method is applied to counts of wage claim benefits, stock market iceberg orders and civilian deaths in Iraq, with bootstrap methods used to quantify sampling variation in the estimated forecast distributions.
A Class of Stochastic Volatility Models for Environmental Applications
, 2010
"... Many environmental data sets have a continuous domain, in time and/or space, and complex features that may be poorly modeled with a stationary Gaussian process (GP). We adapt stochastic volatility modeling to this context, resulting in a stochastic heteroscedastic process (SHP), which is uncondition ..."
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Many environmental data sets have a continuous domain, in time and/or space, and complex features that may be poorly modeled with a stationary Gaussian process (GP). We adapt stochastic volatility modeling to this context, resulting in a stochastic heteroscedastic process (SHP), which is unconditionally stationary and nonGaussian. Conditional on a latent GP, the SHP is a heteroscedastic GP with nonstationary covariance structure. The realizations from SHP are versatile and can represent spatial inhomogeneities. The unconditional correlation functions of SHP form a rich isotropic class that can allow for a smoothed nugget effect. We apply an importance sampling strategy to implement pseudo maximum likelihoodparameter estimation fortheSHP.Topredicttheprocessat unobservedlocations, we develop a plugin best predictor. We extend the singlerealization SHP model to handle replicates across time of SHP realizations in space. Empirical results with simulated data show that SHP is nearly as efficient as GP in outofsample prediction when the true process is stationary GP, and outperforms GP substantially when the true process is SHP. The SHP methodology is applied to enhanced vegetation index data and U.S. NO3 deposition data for illustration.
ShortTerm Wind Speed Forecasting for Power System Operations
, 2011
"... Global large scale penetration of wind energy is accompanied by significant challenges due to the intermittent and unstable nature of wind. High quality shortterm wind speed forecasting is critical to reliable and secure power system operations. This paper gives an overview of the current status of ..."
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Global large scale penetration of wind energy is accompanied by significant challenges due to the intermittent and unstable nature of wind. High quality shortterm wind speed forecasting is critical to reliable and secure power system operations. This paper gives an overview of the current status of worldwide wind power developments and future trends, and reviews some statistical shortterm wind speed forecasting models, including traditional time series models and advanced spacetime statistical models. It also discusses the evaluation of forecast accuracy, in particular the need for realistic loss functions. New challenges in wind speed forecasting regarding ramp events and offshore wind farms are also presented.