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Seasonal climate forecasts are commonly based on model runs from fully coupled forecasting systems that use Earth system models to represent interactions between the atmosphere, ocean, land and other Earth-system components. Recently, machine learning (ML) methods are increasingly being investigated for this task where large-scale climate variability is linked to local or regional temperature or precipitation in a linear or non-linear fashion. This paper investigates the use of interpretable ML methods to predict seasonal precipitation for East Africa in an operational setting. Dimension reduction is performed by decomposing the precipitation fields via empirical orthogonal functions (EOFs), such that only the respective factor loadings need to the predicted. Indices of large-scale climate variability--including the rate of change in individual indices as well as interactions between different indices--are then used as potential features to obtain tercile forecasts from an interpretable ML algorithm. Several research questions regarding the use of data and the effect of model complexity are studied. The results are compared against the ECMWF seasonal forecasting system (SEAS5) for three seasons--MAM, JJAS and OND--over the period 1993-2020. Compared to climatology for the same period, the ECMWF forecasts have negative skill in MAM and JJAS and significant positive skill in OND. The ML approach is on par with climatology in MAM and JJAS and a significantly positive skill in OND, if not quite at the level of the OND ECMWF forecast.

Factor models have become a common and valued tool for understanding the risks associated with an investing strategy. In this report we describe Exabel's factor model, we quantify the fraction of the variability of the returns explained by the different factors, and we show some examples of annual returns of portfolios with different factor exposure.

Quantifying both historic and future volatility is key in portfolio risk management. This note presents and compares estimation strategies for volatility estimation in an estimation universe consisting on 28 629 unique companies from February 2010 to April 2021, with 858 different portfolios. The estimation methods are compared in terms of how they rank the volatility of the different subsets of portfolios. The overall best performing approach estimates volatility from direct entity returns using a GARCH model for variance estimation.

Agricultural food production and natural ecological systems depend on a range of seasonal climate indicators that describe seasonal patterns in climatological conditions. This paper proposes a probabilistic forecasting framework for predicting the end of the freeze-free season, or the time to a mean daily near-surface air temperature below 0 $^\circ$C (here referred to as hard freeze). The forecasting framework is based on the multi-model seasonal forecast ensemble provided by the Copernicus Climate Data Store and uses techniques from survival analysis for time-to-event data. The original mean daily temperature forecasts are statistically post-processed with a mean and variance correction of each model system before the time-to-event forecast is constructed. In a case study for a region in Fennoscandia covering Norway for the period 1993-2020, the proposed forecasts are found to outperform a climatology forecast from an observation-based data product at locations where the average predicted time to hard freeze is less than 40 days after the initialization date of the forecast on October 1.

Probabilistic forecasts of wind speed are important for a wide range of applications, ranging from operational decision making in connection with wind power generation to storm warnings, ship routing and aviation. We present a statistical method that provides locally calibrated, probabilistic wind speed forecasts at any desired place within the forecast domain based on the output of a numerical weather prediction (NWP) model. Three approaches for wind speed post-processing are proposed, which use either truncated normal, gamma or truncated logistic distributions to make probabilistic predictions about future observations conditional on the forecasts of an ensemble prediction system (EPS). In order to provide probabilistic forecasts on a grid, predictive distributions that were calibrated with local wind speed observations need to be interpolated. We study several interpolation schemes that combine geostatistical methods with local information on annual mean wind speeds, and evaluate the proposed methodology with surface wind speed forecasts over Germany from the COSMO-DE (Consortium for Small-scale Modelling) ensemble prediction system., Comment: Published at http://dx.doi.org/10.1214/15-AOAS843 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Statistical postprocessing techniques are commonly used to improve the skill of ensembles of numerical weather forecasts. This paper considers spatial extensions of the well-established nonhomogeneous Gaussian regression (NGR) postprocessing technique for surface temperature and a recent modification thereof in which the local climatology is included in the regression model for a locally adaptive postprocessing. In a comparative study employing 21 h forecasts from the COSMO-DE ensemble predictive system over Germany, two approaches for modeling spatial forecast error correlations are considered: A parametric Gaussian random field model and the ensemble copula coupling approach which utilizes the spatial rank correlation structure of the raw ensemble. Additionally, the NGR methods are compared to both univariate and spatial versions of the ensemble Bayesian model averaging (BMA) postprocessing technique.

Any decision making process that relies on a probabilistic forecast of future events necessarily requires a calibrated forecast. This paper proposes new methods for empirically assessing forecast calibration in a multivariate setting where the probabilistic forecast is given by an ensemble of equally probable forecast scenarios. Multivariate properties are mapped to a single dimension through a pre-rank function and the calibration is subsequently assessed visually through a histogram of the ranks of the observation's pre-ranks. Average ranking assigns a pre-rank based on the average univariate rank while band depth ranking employs the concept of functional band depth where the centrality of the observation within the forecast ensemble is assessed. Several simulation examples and a case study of temperature forecast trajectories at Berlin Tegel Airport in Germany demonstrate that both multivariate ranking methods can successfully detect various sources of miscalibration and scale efficiently to high dimensional settings.

Statistical post-processing of dynamical forecast ensembles is an essential component of weather forecasting. In this article, we present a post-processing method that generates full predictive probability distributions for precipitation accumulations based on ensemble model output statistics (EMOS). We model precipitation amounts by a generalized extreme value distribution that is left-censored at zero. This distribution permits modelling precipitation on the original scale without prior transformation of the data. A closed form expression for its continuous rank probability score can be derived and permits computationally efficient model fitting. We discuss an extension of our approach that incorporates further statistics characterizing the spatial variability of precipitation amounts in the vicinity of the location of interest. The proposed EMOS method is applied to daily 18-h forecasts of 6-h accumulated precipitation over Germany in 2011 using the COSMO-DE ensemble prediction system operated by the German Meteorological Service. It yields calibrated and sharp predictive distributions and compares favourably with extended logistic regression and Bayesian model averaging which are state of the art approaches for precipitation post-processing. The incorporation of neighbourhood information further improves predictive performance and turns out to be a useful strategy to account for displacement errors of the dynamical forecasts in a probabilistic forecasting framework.

We propose an extension of the non-homogeneous Gaussian regression (NGR) model by Gneiting et al. (2005) that yields locally calibrated probabilistic forecasts of tem- perature, based on the output of an ensemble prediction system (EPS). Our method represents the mean of the predictive distributions as a sum of short-term averages of local temperatures and EPS-driven terms. For the spatial interpolation of temperature averages and local forecast uncertainty parameters we use a Gaussian random field model with an intrinsically stationary component that captures large scale fluctuations and a location-dependent nugget effect that accounts for small scale variability. Based on the dynamical forecasts by the COSMO-DE-EPS and observational data over Germany we evaluate the performance of our method and and compare it with other post-processing approaches such as geostatistical model averaging. Our method yields locally calibrated and sharp probabilistic forecasts and compares favorably with other approaches. It is reasonably simple, computationally efficient, and therefore suitable for operational usage in the post-processing of temperature ensemble forecasts.