4,811 research outputs found
Calibration tests for multivariate Gaussian forecasts
Forecasts by nature should take the form of probabilistic distributions. Calibration, the statistical consistency of forecast distributions and observations, is a central property of good probabilistic forecasts. Calibration of univariate forecasts has been widely discussed, and significance tests are commonly used to investigate whether a prediction model is miscalibrated. However, calibration tests for multivariate forecasts are rare. In this paper, we propose calibration tests for multivariate Gaussian forecasts based on two types of the Dawid–Sebastiani score (DSS): the multivariate DSS (mDSS) and the individual DSS (iDSS). Analytic results and simulation studies show that the tests have sufficient power to detect miscalibrated forecasts with incorrect mean or incorrect variance. But for forecasts with incorrect correlation coefficients, only the tests based on mDSS are sensitive to miscalibration. As an illustration, we apply the methodology to weekly data on Norovirus disease incidence among males and females in Germany, in 2011–2014. The results further show that tests for multivariate forecasts are useful tools and superior to univariate calibration tests for correlated multivariate forecasts
Statistical post-processing of hydrological forecasts using Bayesian model averaging
Accurate and reliable probabilistic forecasts of hydrological quantities like
runoff or water level are beneficial to various areas of society. Probabilistic
state-of-the-art hydrological ensemble prediction models are usually driven
with meteorological ensemble forecasts. Hence, biases and dispersion errors of
the meteorological forecasts cascade down to the hydrological predictions and
add to the errors of the hydrological models. The systematic parts of these
errors can be reduced by applying statistical post-processing. For a sound
estimation of predictive uncertainty and an optimal correction of systematic
errors, statistical post-processing methods should be tailored to the
particular forecast variable at hand. Former studies have shown that it can
make sense to treat hydrological quantities as bounded variables. In this
paper, a doubly truncated Bayesian model averaging (BMA) method, which allows
for flexible post-processing of (multi-model) ensemble forecasts of water
level, is introduced. A case study based on water level for a gauge of river
Rhine, reveals a good predictive skill of doubly truncated BMA compared both to
the raw ensemble and the reference ensemble model output statistics approach.Comment: 19 pages, 6 figure
Measuring output gap uncertainty
We propose a methodology for producing density forecasts for the output gap in real time using a large number of vector autoregessions in inflation and output gap measures. Density combination utilizes a linear mixture of experts framework to produce potentially non-Gaussian ensemble densities for the unobserved output gap. In our application, we show that data revisions alter substantially our probabilistic assessments of the output gap using a variety of output gap measures derived from univariate detrending filters. The resulting ensemble produces well-calibrated forecast densities for US inflation in real time, in contrast to those from simple univariate autoregressions which ignore the contribution of the output gap. Combining evidence from both linear trends and more flexible univariate detrending filters induces strong multi-modality in the predictive densities for the unobserved output gap. The peaks associated with these two detrending methodologies indicate output gaps of opposite sign for some observations, reflecting the pervasive nature of model uncertainty in our US data
Real-Time Multivariate Density Forecast Evaluation and Calibration: Monitoring the Risk of High-Frequency Returns on Foreign Exchange
We provide a framework for evaluating and improving multivariate density forecasts. Among other things, the multivariate framework lets us evaluate the adequacy of density forecasts involving cross-variable interactions, such as time-varying conditional correlations. We also provide conditions under which a technique of density forecast "calibration" can be used to improve deficient density forecasts. Finally, motivated by recent advances in financial risk management, we provide a detailed application to multivariate high-frequency exchange rate density forecasts. Copyright © 1998 F.X. Diebold, J. Hahn, and A.S. Tay. This paper is also available at
Forecasting and prequential validation for time varying meta-elliptical distributions
We consider forecasting and prequential (predictive sequential) validation of meta-elliptical distributions with time varying parameters. Using the weak prequential principle of Dawid, we conduct model validation avoiding nuisance parameter problems. Results rely on the structure of meta-elliptical distributions and we allow for discontinuities in the marginals and time varying parameters. We illustrate the ideas of the paper using a large data set of 16 commodity prices
Generation and Evaluation of Space-Time Trajectories of Photovoltaic Power
In the probabilistic energy forecasting literature, emphasis is mainly placed
on deriving marginal predictive densities for which each random variable is
dealt with individually. Such marginals description is sufficient for power
systems related operational problems if and only if optimal decisions are to be
made for each lead-time and each location independently of each other. However,
many of these operational processes are temporally and spatially coupled, while
uncertainty in photovoltaic (PV) generation is strongly dependent in time and
in space. This issue is addressed here by analysing and capturing
spatio-temporal dependencies in PV generation. Multivariate predictive
distributions are modelled and space-time trajectories describing the potential
evolution of forecast errors through successive lead-times and locations are
generated. Discrimination ability of the relevant scoring rules on performance
assessment of space-time trajectories of PV generation is also studied.
Finally, the advantage of taking into account space-time correlations over
probabilistic and point forecasts is investigated. The empirical investigation
is based on the solar PV dataset of the Global Energy Forecasting Competition
(GEFCom) 2014.Comment: 33 pages, 11 Figure
The past, present, and future of macroeconomic forecasting
Broadly defined, macroeconomic forecasting is alive and well. Nonstructural forecasting, which is based largely on reduced-form correlations, has always been well and continues to improve. Structural forecasting, which aligns itself with economic theory and, hence, rises and falls with theory, receded following the decline of Keynesian theory. In recent years, however, powerful new dynamic stochastic general equilibrium theory has been developed, and structural macroeconomic forecasting is poised for resurgence.Forecasting
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