arXiv subjects

Tilmann Gneiting

Publications and source records attributed to Tilmann Gneiting.

41 records · Page 3Linked to original sources

arXiv2011

Combining Predictive Distributions

Predictive distributions need to be aggregated when probabilistic forecasts are merged, or when expert opinions expressed in terms of probability distributions are fused. We take a prediction space approach that applies to discrete, mixed discrete-continuous and continuous predictive distributions alike, and study combination formulas for cumulative distribution functions from the perspectives of coherence, probabilistic and conditional calibration, and dispersion. Both linear and non-linear aggregation methods are investigated, including generalized, spread-adjusted and beta-transformed linear pools. The effects and techniques are demonstrated theoretically, in simulation examples, and in case studies on density forecasts for S&P 500 returns and daily maximum temperature at Seattle-Tacoma Airport.

math.ST↗

arXiv2010

Predicting Inflation: Professional Experts Versus No-Change Forecasts

We compare forecasts of United States inflation from the Survey of Professional Forecasters (SPF) to predictions made by simple statistical techniques. In nowcasting, economic expertise is persuasive. When projecting beyond the current quarter, novel yet simplistic probabilistic no-change forecasts are equally competitive. We further interpret surveys as ensembles of forecasts, and show that they can be used similarly to the ways in which ensemble prediction systems have transformed weather forecasting. Then we borrow another idea from weather forecasting, in that we apply statistical techniques to postprocess the SPF forecast, based on experience from the recent past. The foregoing conclusions remain unchanged after survey postprocessing.

stat.AP↗

arXiv2010

Making and Evaluating Point Forecasts

Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, such as the absolute error or the squared error. The individual scores are then averaged over forecast cases, to result in a summary measure of the predictive performance, such as the mean absolute error or the (root) mean squared error. I demonstrate that this common practice can lead to grossly misguided inferences, unless the scoring function and the forecasting task are carefully matched. Effective point forecasting requires that the scoring function be specified ex ante, or that the forecaster receives a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. If the scoring function is specified ex ante, the forecaster can issue the optimal point forecast, namely, the Bayes rule. If the forecaster receives a directive in the form of a functional, it is critical that the scoring function be consistent for it, in the sense that the expected score is minimized when following the directive. A functional is elicitable if there exists a scoring function that is strictly consistent for it. Expectations, ratios of expectations and quantiles are elicitable. For example, a scoring function is consistent for the mean functional if and only if it is a Bregman function. It is consistent for a quantile if and only if it is generalized piecewise linear. Similar characterizations apply to ratios of expectations and to expectiles. Weighted scoring functions are consistent for functionals that adapt to the weighting in peculiar ways. Not all functionals are elicitable; for instance, conditional value-at-risk is not, despite its popularity in quantitative finance.

math.ST↗

arXiv2009

Probabilistic quantitative precipitation field forecasting using a two-stage spatial model

Short-range forecasts of precipitation fields are needed in a wealth of agricultural, hydrological, ecological and other applications. Forecasts from numerical weather prediction models are often biased and do not provide uncertainty information. Here we present a postprocessing technique for such numerical forecasts that produces correlated probabilistic forecasts of precipitation accumulation at multiple sites simultaneously. The statistical model is a spatial version of a two-stage model that represents the distribution of precipitation by a mixture of a point mass at zero and a Gamma density for the continuous distribution of precipitation accumulation. Spatial correlation is captured by assuming that two Gaussian processes drive precipitation occurrence and precipitation amount, respectively. The first process is latent and drives precipitation occurrence via a threshold. The second process explains the spatial correlation in precipitation accumulation. It is related to precipitation via a site-specific transformation function, so as to retain the marginal right-skewed distribution of precipitation while modeling spatial dependence. Both processes take into account the information contained in the numerical weather forecast and are modeled as stationary isotropic spatial processes with an exponential correlation function. The two-stage spatial model was applied to 48-hour-ahead forecasts of daily precipitation accumulation over the Pacific Northwest in 2004. The predictive distributions from the two-stage spatial model were calibrated and sharp, and outperformed reference forecasts for spatially composite and areally averaged quantities.

stat.AP↗

arXiv2001

Stochastic models which separate fractal dimension and Hurst effect

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal dimension, a measure of roughness, and Hurst coefficient, a measure of long-memory dependence. This letter introduces simple stochastic models which allow for any combination of fractal dimension and Hurst exponent. We synthesize images from these models, with arbitrary fractal properties and power-law correlations, and propose a test for self-similarity.

physics.data-an↗