Value at Risk (VaR) forecasts can be produced from conditional autoregressive VaR models, estimated using quantile regression. Quantile modeling avoids a distributional assumption, and allows the ...dynamics of the quantiles to differ for each probability level. However, by focusing on a quantile, these models provide no information regarding expected shortfall (ES), which is the expectation of the exceedances beyond the quantile. We introduce a method for predicting ES corresponding to VaR forecasts produced by quantile regression models. It is well known that quantile regression is equivalent to maximum likelihood based on an asymmetric Laplace (AL) density. We allow the density's scale to be time-varying, and show that it can be used to estimate conditional ES. This enables a joint model of conditional VaR and ES to be estimated by maximizing an AL log-likelihood. Although this estimation framework uses an AL density, it does not rely on an assumption for the returns distribution. We also use the AL log-likelihood for forecast evaluation, and show that it is strictly consistent for the joint evaluation of VaR and ES. Empirical illustration is provided using stock index data. Supplementary materials for this article are available online.
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BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
Plasmonic gold nanorod instability and reshaping behavior below melting points are important for many future applications but are yet to be fully understood, with existing nanoparticle melting ...theories unable to explain the observations. Here, we have systematically studied the photothermal reshaping behavior of gold nanorods irradiated with femtosecond laser pulses to report that the instability is driven by curvature-induced surface diffusion rather than a threshold melting process, and that the stability dramatically decreases with increasing aspect ratio. We successfully utilized the surface diffusion model to explain the observations and found that the activation energy for surface diffusion was dependent on the aspect ratio of the rods, from 0.6 eV for aspect ratio of 5 to 1.5 eV for aspect ratio less than 3. This result indicates that the surface atoms are much easier to diffuse around in larger aspect ratio rods than in shorter rods and can induce reshaping at any given temperature. Current plasmonics and nanorod applications with the sharp geometric features used for greater field enhancement will therefore need to consider surface diffusion driven shape change even at low temperatures.
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•Autoregressive logit models are developed for wind power ramp prediction.•Short-term probability forecasts are generated.•The models are applied to wind power time series from four wind farms.•The ...new models outperform benchmark methods.
A challenge for the efficient operation of power systems and wind farms is the occurrence of wind power ramps, which are sudden large changes in the power output from a wind farm. This paper considers the probabilistic forecasting of a ramp event, defined as exceedance beyond a specified threshold. We directly model the exceedance probability using autoregressive logit models fitted to the change in wind power. These models can be estimated by maximising a Bernoulli likelihood. We introduce a model that simultaneously estimates the ramp event probabilities for different thresholds using a multinomial logit structure and categorical distribution. To model jointly the probability of ramp events at more than one wind farm, we develop a multinomial logit formulation, with parameters estimated using a bivariate Bernoulli distribution. We use a similar approach in a model for jointly predicting one and two steps-ahead. We evaluate post-sample probability forecast accuracy using hourly wind power data from four wind farms.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Online short-term load forecasting is needed for the real-time scheduling of electricity generation. Univariate methods have been developed that model the intraweek and intraday seasonal cycles in ...intraday load data. Three such methods, shown to be competitive in recent empirical studies, are double seasonal ARMA, an adaptation of Holt–Winters exponential smoothing for double seasonality, and another, recently proposed, exponential smoothing method. In multiple years of load data, in addition to intraday and intraweek cycles, an intrayear seasonal cycle is also apparent. We extend the three double seasonal methods in order to accommodate the intrayear seasonal cycle. Using six years of British and French data, we show that for prediction up to a day-ahead the triple seasonal methods outperform the double seasonal methods, and also a univariate neural network approach. Further improvement in accuracy is produced by using a combination of the forecasts from two of the triple seasonal methods.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
The recent advent of smart meters has led to large micro-level datasets. For the first time, the electricity consumption at individual sites is available on a near real-time basis. Efficient ...management of energy resources, electric utilities, and transmission grids, can be greatly facilitated by harnessing the potential of this data. The aim of this study is to generate probability density estimates for consumption recorded by individual smart meters. Such estimates can assist decision making by helping consumers identify and minimize their excess electricity usage, especially during peak times. For suppliers, these estimates can be used to devise innovative time-of-use pricing strategies aimed at their target consumers. We consider methods based on conditional kernel density (CKD) estimation with the incorporation of a decay parameter. The methods capture the seasonality in consumption, and enable a nonparametric estimation of its conditional density. Using 8 months of half-hourly data for 1000 meterswe evaluate point and density forecasts, for lead times ranging from one half-hour up to a week ahead. We find that the kernel-based methods outperform a simple benchmark method that does not account for seasonality, and compare well with an exponential smoothing method that we use as a sophisticated benchmark. To gauge the financial impact, we use density estimates of consumption to derive prediction intervals of electricity cost for different time-of-use tariffs. We show that a simple strategy of switching between different tariffs, based on a comparison of cost densities, delivers significant cost savings for the great majority of consumers.
•We generate density forecasts for electricity consumption recorded by smart meters.•Methods based on Conditional Kernel Density (CKD) estimation are considered.•CKD methods can accommodate the seasonality in consumption time series.•We derive prediction interval of electricity cost for different time-of-use tariffs.•Switching between tariffs based on a comparison of cost densities delivers savings.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
A joint model for the Value at Risk (VaR) and expected shortfall (ES) can be estimated using a joint scoring function. Previous work has modelled the ES as the product of the VaR and a constant ...factor. However, this implies the same dynamics for the ES and the VaR. We propose a time-varying multiplicative factor. The ES has been expressed as the product of an expectile and a constant factor that depends on the expectile level. We rewrite this as the product of a quantile and a function of a time-varying expectile level. The expectile level is a function of the Omega ratio, which is the ratio of the expected gain to the expected loss. This leads us to model the ES as the product of the VaR and a factor that is a function of a time-varying Omega ratio. We provide empirical support using stock indices and individual stocks.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Combining provides a pragmatic way of synthesising the information provided by individual forecasting methods. In the context of forecasting the mean, numerous studies have shown that combining often ...leads to improvements in accuracy. Despite the importance of the value at risk (VaR), though, few papers have considered quantile forecast combinations. One risk measure that is receiving an increasing amount of attention is the expected shortfall (ES), which is the expectation of the exceedances beyond the VaR. There have been no previous studies on combining ES predictions, presumably due to there being no suitable loss function for ES. However, it has been shown recently that a set of scoring functions exist for the joint estimation or backtesting of VaR and ES forecasts. We use such scoring functions to estimate combining weights for VaR and ES prediction. The results from five stock indices show that combining outperforms the individual methods for the 1% and 5% probability levels.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•A case-study on short-term load forecasting for France is presented.•Load observed on normal and special days is modelled using a unified framework.•Each special day is treated as having a unique ...load profile.•Subjective judgment is incorporated during modelling using a rule-based approach.•Model evaluation is based on a comparison of point and density forecast accuracy.
This paper presents a case study on short-term load forecasting for France, with emphasis on special days, such as public holidays. We investigate the generalisability to French data of a recently proposed approach, which generates forecasts for normal and special days in a coherent and unified framework, by incorporating subjective judgment in univariate statistical models using a rule-based methodology. The intraday, intraweek, and intrayear seasonality in load are accommodated using a rule-based triple seasonal adaptation of a seasonal autoregressive moving average (SARMA) model. We find that, for application to French load, the method requires an important adaption. We also adapt a recently proposed SARMA model that accommodates special day effects on an hourly basis using indicator variables. Using a rule formulated specifically for the French load, we compare the SARMA models with a range of different benchmark methods based on an evaluation of their point and density forecast accuracy. As sophisticated benchmarks, we employ the rule-based triple seasonal adaptations of Holt-Winters-Taylor (HWT) exponential smoothing and artificial neural networks (ANNs). We use nine years of half-hourly French load data, and consider lead times ranging from one half-hour up to a day ahead. The rule-based SARMA approach generated the most accurate forecasts.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
•Interval and distributional forecast combinations at the state and national level.•Combining considered with frequent entry and exit of forecasting teams.•Weighted combining proposed, based on ...inverse of interval and distribution scores.•For early periods, the median of the available forecasts was most effective.•For later periods, weighting the forecasts was the most accurate combination.
The COVID-19 pandemic has placed forecasting models at the forefront of health policy making. Predictions of mortality, cases and hospitalisations help governments meet planning and resource allocation challenges. In this paper, we consider the weekly forecasting of the cumulative mortality due to COVID-19 at the national and state level in the U.S. Optimal decision-making requires a forecast of a probability distribution, rather than just a single point forecast. Interval forecasts are also important, as they can support decision making and provide situational awareness. We consider the case where probabilistic forecasts have been provided by multiple forecasting teams, and we combine the forecasts to extract the wisdom of the crowd. We use a dataset that has been made publicly available from the COVID-19 Forecast Hub. A notable feature of the dataset is that the availability of forecasts from participating teams varies greatly across the 40 weeks in our study. We evaluate the accuracy of combining methods that have been previously proposed for interval forecasts and predictions of probability distributions. These include the use of the simple average, the median, and trimming methods. In addition, we propose several new weighted combining methods. Our results show that, although the median was very useful for the early weeks of the pandemic, the simple average was preferable thereafter, and that, as a history of forecast accuracy accumulates, the best results can be produced by a weighted combining method that uses weights that are inversely proportional to the historical accuracy of the individual forecasting teams.
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•A probabilistic decision model is proposed to dispatch a turbine maintenance vessel.•Statistical models are presented for wave height, the key variable in the decision.•Models are evaluated in terms ...of statistical measures as well as the impact on cost.•The sensitivity of the results is examined under various cost conditions.
Wind power continues to be the fastest growing source of renewable energy. This paper is concerned with the timing of offshore turbine maintenance for a turbine that is no longer functioning. Service vehicle access is limited by the weather, with wave height being the important factor in deciding whether access can be achieved safely. If the vehicle is mobilized, but the wave height then exceeds the safe limit, the journey is wasted. Conversely, if the vehicle is not mobilized, and the wave height then does not exceed the limit, the opportunity to repair the turbine has been wasted. Previous work has based the decision as to whether to mobilize a service vessel on point forecasts for wave height. In this paper, we incorporate probabilistic forecasting to enable rational decision making by the maintenance engineers, and to improve situational awareness regarding risk. We show that, in terms of minimizing expected cost, the decision as to whether to send the service vessel depends on the value of the probability of wave height falling below the safe limit. We produce forecasts of this probability using time series methods specifically designed for generating wave height density forecasts, including ARMA-GARCH models. We evaluate the methods in terms of statistical probability forecast accuracy, as well as monetary impact, and we examine the sensitivity of the results to different values of the costs.
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