Accuracy Of Point Forecasts Research Articles

Forecasting Age- and Sex-Specific Survival Functions: Application to Annuity Pricing

We introduce the function principal component regression (FPCR) forecasting method to model and forecast age-specific survival functions observed over time. The age distribution of survival functions is an example of constrained data whose values lie within a unit interval. Because of the constraint, such data do not reside in a linear vector space. A natural way to deal with such a constraint is through an invertible logit transformation that maps constrained onto unconstrained data in a linear space. With a time series of unconstrained data, we apply a functional time-series forecasting method to produce point and interval forecasts. The forecasts are then converted back to the original scale via the inverse logit transformation. Using the age- and sex-specific survival functions for Australia, we investigate the point and interval forecast accuracies for various horizons. We conclude that the functional principal component regression (FPCR) provides better forecast accuracy than the Lee–Carter (LC) method. Therefore, we apply FPCR to calculate annuity pricing and compare it with the market annuity price.

Model selection for long-term load forecasting under uncertainty

Purpose The purpose of this study is to propose a systematic model selection procedure for long-term load forecasting (LTLF) for ex-ante and ex-post cases considering uncertainty in exogenous predictors. Design/methodology/approach The different variants of regression models, namely, Polynomial Regression (PR), Generalised Additive Model (GAM), Quantile Polynomial Regression (QPR) and Quantile Spline Regression (QSR), incorporating uncertainty in exogenous predictors like population, Real Gross State Product (RGSP) and Real Per Capita Income (RPCI), temperature and indicators of breakpoints and calendar effects, are considered for LTLF. Initially, the Backward Feature Elimination procedure is used to identify the optimal set of predictors for LTLF. Then, the consistency in model accuracies is evaluated using point and probabilistic forecast error metrics for ex-ante and ex-post cases. Findings From this study, it is found PR model outperformed in ex-ante condition, while QPR model outperformed in ex-post condition. Further, QPR model performed consistently across validation and testing periods. Overall, QPR model excelled in capturing uncertainty in exogenous predictors, thereby reducing over-forecast error and risk of overinvestment. Research limitations/implications These findings can help utilities to align model selection strategies with their risk tolerance. Originality/value To propose the systematic model selection procedure in this study, the consistent performance of PR, GAM, QPR and QSR models are evaluated using point forecast accuracy metrics Mean Absolute Percentage Error, Root Mean Squared Error and probabilistic forecast accuracy metric Pinball Score for ex-ante and ex-post cases considering uncertainty in the considered exogenous predictors such as RGSP, RPCI, population and temperature.

Generative deep learning for probabilistic streamflow forecasting: Conditional variational auto-encoder

Probabilistic hydrological forecasting has gained increasing importance in recent years, as it offers essential information for risk-based decision-making and flood management. Traditional hydrological models often produce deterministic forecasts, which do not account for the inherent uncertainties in hydrological systems. Although many previous studies have investigated using deep learning (DL) models for hydrological prediction, the development of probabilistic DL models (especially, generative models) has not yet been thoroughly examined for hydrological forecasting. The present study investigates the efficacy of a generative DL model, namely, conditional variational auto-encoder (CVAE). CVAE is applied for one-seven day(s) ahead probabilistic streamflow forecasting in 75 basins from the Canadian model parameter experiment (CANOPEX) database. The CVAE forecast model, which outputs forecasts in the form of a probability distribution, was benchmarked against two state-of-the-art quantile-based DL models: quantile-based encoder-decoder (ED) and quantile-based CVAE (QCVAE). The latter outputs forecasts for specific quantiles of a probability distribution (here, q = 0.05, 0.5, 0.95). More than 9000 models were developed based on different basins, input variable sets, and model structures. The models were evaluated in terms of point forecast accuracy and forecast reliability. The results indicate that the CVAE model generally outperforms the benchmark models in terms of reliability at a 90 % confidence level (median reliability of 92.49 % compared to 87.35 % and 84.59 % for ED and QCVAE, respectively). However, the quantile-based forecast models produce slightly more accurate point forecasts than the CVAE (median Kling-Gupta efficiency (KGE) of 0.88 compared to 0.90 for both ED and QCVAE). Notably, the CVAE model exhibits superior probabilistic forecasts in basins with poor point forecast accuracy, highlighting its usefulness over benchmark methods in difficult-to-forecast basins. Overall, CVAE is a promising probabilistic DL model for streamflow forecasting, and it can be readily applied for forecasting other hydrological variables (evapotranspiration, water level, etc.). The findings of this study provide a basis for future research on probabilistic forecasting of hydrological variables using generative DL models.

A multiplicative Holt–Winters model and autoregressive moving-average for hyponatremia mortality rates

This study presents the effective utilization of data analysis in efficiently managing medical resources — a crucial factor in ensuring high-quality healthcare delivery and positive patient outcomes. We employ a multiplicative Holt-Winters model and a linear model with an autoregressive moving-average time series error term and analyze time series mortality rates associated with hyponatremia, a condition that leads to a systemic electrolyte imbalance. The time series data consistently reveals noticeable trends and recurring seasonal patterns. To address these intricate patterns, the proposed data analysis approaches adeptly incorporate these features, thereby yielding relatively accurate point forecasts and reliable forecast intervals. Beyond mere forecasting, the autoregressive moving-average model approach offers insights into the overarching trend and facilitates the comparison of seasonal components. One of the approaches is well-suited for the specific time series related to hyponatremia and holds the potential for extension to incorporate more complex trends beyond linearity. The research demonstrates the synergistic relationship between data analysis and medical expertise, working in tandem to achieve the optimal allocation of medical resources. We strongly advocate for the routine integration of statistical analyses as an essential practice to foster this harmonious synergy.

Diffusion‐based conditional wind power forecasting via channel attention

AbstractWind energy is one of the most significant renewable sources of energy while accurate and reliable wind power forecasting methods may greatly benefit power system planning and scheduling. Recently, many machine learning algorithms have shown significant advantages in how to extract temporal features for wind power forecasting. However, wind power curves in the time domain frequently display intermittent features and significant uncertainty, which is not favorable to precise and reliable forecasting. In this paper, the Diffusion and Channel Attention‐based Wind Power Forecasting (DC‐WPF) framework is proposed, which transforms wind power data into the frequency domain while applying advanced channel attention techniques to aid the model in capturing the frequency domain information and ultimately enhancing accuracy. With high‐accuracy results, DC‐WPF then proposes a diffusion‐based framework to transform the point forecasting results into probabilistic forecasts to capture the uncertainty. Finally, extensive experiments on six wind power plants show that our method can improve the point forecasting accuracy of wind power and provide advanced probabilistic forecasts at a multi‐time scale.

Time to build a new practice of foresight for national economies? Ireland, and uncertain futures in forecasts and scenarios

PurposeThe literature on economic forecasting, is showing an increase in criticism, of the inaccuracy of forecasts, with major implications for economic, and fiscal policymaking. Forecasts are subject to the systemic uncertainty of human systems, considerable event-driven uncertainty, and show biases towards optimistic growth paths. The purpose of this study is to consider approaches to improve economic foresight.Design/methodology/approachThis study describes the practice of economic foresight as evolving in two separate, non-overlapping branches, short-term economic forecasting, and long-term scenario analysis of development, the latter found in studies of climate change and sustainability. The unique case of Ireland is considered, a country that has experienced both steep growth and deep troughs, with uncertainty that has confounded forecasting. The challenges facing forecasts are discussed, with brief review of the drivers of growth, and of long-term economic scenarios in the global literature.FindingsEconomic forecasting seeks to manage uncertainty by improving the accuracy of quantitative point forecasts, and related models. Yet, systematic forecast failures remain, and the economy defies prediction, even in the near-term. In contrast, long-term scenario analysis eschews forecasts in favour of a set of plausible or possible alternative scenarios. Using alternative scenarios is a response to the irreducible uncertainty of complex systems, with sophisticated approaches employed to integrate qualitative and quantitative insights.Research limitations/implicationsTo support economic and fiscal policymaking, it is necessary support advancement in approaches to economic foresight, to improve handling of uncertainty and related risk.Practical implicationsWhile European Union Regulation (EC) 1466/97 mandates pursuit of improved accuracy, in short-term economic forecasts, there is now a case for implementing advanced foresight approaches, for improved analysis, and more robust decision-making.Social implicationsBuilding economic resilience and adaptability, as part of a sustainable future, requires both long-term strategic planning, and short-term policy. A 21st century policymaking process can be better supported by analysis of alternative scenarios.Originality/valueTo the best of the authors’ knowledge, the article is original in considering the application of scenario foresight approaches, in economic forecasting. The study has value in improving the baseline forecast methods, that are fundamental to contemporary economics, and in bringing the field of economics into the heart of foresight.

Development and evaluation of probabilistic forecasting methods for small area populations

Planning and development decisions in both the government and business sectors often require small area population forecasts. Unfortunately, current methods often produce forecasts that are inaccurate, particularly for remote areas and those with smaller populations. Such inaccuracy necessitates the development and evaluation of methods to forecast and communicate forecast uncertainty, however, little research has been conducted in this domain for small area populations. In this paper, we evaluate a set of probabilistic forecasting methods which include Autoregressive integrated moving average, Exponential Smoothing, THETA, LightGBM and XGBOOST, to produce point forecasts and 80% prediction intervals for Australian SA2 small area populations. We also investigate methods to combine the intervals to produce ensemble forecasts. Our results show that individual probabilistic methods generally produce prediction intervals which underestimate forecast uncertainty. Combining forecasts improves the overall accuracy of point forecasts and the coverage of their intervals, however, coverage still tends to be less than the expected 80% for all but the most conservative combination method.

Probabilistic forecasting of daily COVID-19 admissions using machine learning

Abstract Accepted by: Aris Syntetos Accurate forecasts of daily Coronavirus-2019 (COVID-19) admissions are critical for healthcare planners and decision-makers to better manage scarce resources during and around infection peaks. Numerous studies have focused on forecasting COVID-19 admissions at the national or global levels. Localized predictions are vital, as they allow for resource planning redistribution, but also scarce and harder to get right. Several possible indicators can be used to predict COVID-19 admissions. The inherent variability in the admissions necessitates the generation and evaluation of the forecast distribution of admissions, as opposed to producing only a point forecast. In this study, we propose a quantile regression forest (QRF) model for probabilistic forecasting of daily COVID-19 admissions for a local hospital trust (aggregation of 3 hospitals), up to 7 days ahead, using a multitude of different predictors. We evaluate point forecast accuracy as well as the accuracy of the forecast distribution using appropriate measures. We provide evidence that QRF outperforms univariate time series methods and other more sophisticated benchmarks. Our findings also show that lagged admissions, total positive cases, daily tests performed, and Google grocery and Apple driving are the most salient predictors. Finally, we highlight areas where further research is needed.

Probabilistic forecasting of hourly emergency department arrivals

ABSTRACT An accurate forecast of Emergency Department (ED) arrivals by an hour of the day is critical to meet patients’ demand. It enables planners to match ED staff to the number of arrivals, redeploy staff, and reconfigure units. In this study, we develop a model based on Generalised Additive Models and an advanced dynamic model based on exponential smoothing to generate an hourly probabilistic forecast of ED arrivals for a prediction window of 48 hours. We compare the forecast accuracy of these models against appropriate benchmarks, including TBATS, Poisson Regression, Prophet, and simple empirical distribution. We use Root Mean Squared Error to examine the point forecast accuracy and assess the forecast distribution accuracy using Quantile Bias, PinBall Score and Pinball Skill Score. Our results indicate that the proposed models outperform their benchmarks. Our developed models can also be generalised to other services, such as hospitals, ambulances or clinical desk services.

Deep distributional time series models and the probabilistic forecasting of intraday electricity prices

SummaryRecurrent neural networks (RNNs) with rich feature vectors of past values can provide accurate point forecasts for series that exhibit complex serial dependence. We propose two approaches to constructing deep time series probabilistic models based on a variant of RNN called an echo state network (ESN). The first is where the output layer of the ESN has stochastic disturbances and a Bayesian prior for regularization. The second employs the implicit copula of an ESN with Gaussian disturbances, which is a Gaussian copula process on the feature space. Combining this copula process with a nonparametrically estimated marginal distribution produces a distributional time series model. The resulting probabilistic forecasts are deep functions of the feature vector and marginally calibrated. In both approaches, Markov chain Monte Carlo methods are used to estimate the models and compute forecasts. The proposed models are suitable for the complex task of forecasting intraday electricity prices. Using data from the Australian market, we show that our deep time series models provide accurate short‐term probabilistic price forecasts, with the copula model dominating. Moreover, the models provide a flexible framework for incorporating probabilistic forecasts of electricity demand, which increases upper tail forecast accuracy from the copula model significantly.

Pairing ensemble numerical weather prediction with ensemble physical model chain for probabilistic photovoltaic power forecasting

Under the two-step framework of photovoltaic (PV) power forecasting, that is, forecasting first the irradiance and then converting it to PV power, there are two chief ways in which one can account for the uncertainty embedded in the final PV power forecast. One of those is to produce probabilistic irradiance forecast through, for example, ensemble numerical weather prediction (NWP), and the other is to pass the irradiance forecast through a collection of different irradiance-to-power conversion sequences, which are known as model chains. This work investigates, for the first time, into the question: Whether pairing ensemble NWP with ensemble model chain is better than leveraging any individual method alone? Using data from 14 utility-scale ground-mounted PV plants in Hungary and the state-of-the-art global mesoscale NWP model of the European Centre for Medium-Range Weather Forecasts, it is herein demonstrated that the best probabilistic PV power forecast needs to consider both ensemble NWP and ensemble model chain. Furthermore, owing to the higher-quality probabilistic forecasts, the point forecast accuracy is also improved substantially through pairing. Overall, the recommended paring strategy achieves a mean-normalized continuous ranked probability score and a root mean square error of 18.4% and 42.1%, respectively.

Feature-based intermittent demand forecast combinations: accuracy and inventory implications

Intermittent demand forecasting is a ubiquitous and challenging problem in production systems and supply chain management. In recent years, there has been a growing focus on developing forecasting approaches for intermittent demand from academic and practical perspectives. However, limited attention has been given to forecast combination methods, which have achieved competitive performance in forecasting fast-moving time series. The current study examines the empirical outcomes of some existing forecast combination methods and proposes a generalised feature-based framework for intermittent demand forecasting. The proposed framework has been shown to improve the accuracy of point and quantile forecasts based on two real data sets. Further, some analysis of features, forecasting pools and computational efficiency is also provided. The findings indicate the intelligibility and flexibility of the proposed approach in intermittent demand forecasting and offer insights regarding inventory decisions.

A Novel Hybrid Machine Learning Model for Wind Speed Probabilistic Forecasting

Accurately capturing wind speed fluctuations and quantifying the uncertainties has important implications for energy planning and management. This paper proposes a novel hybrid machine learning model to solve the problem of probabilistic prediction of wind speed. The model couples the light gradient boosting machine (LGB) model with the Gaussian process regression (GPR) model, where the LGB model can provide high-precision deterministic wind speed prediction results, and the GPR model can provide reliable probabilistic prediction results. The proposed model was applied to predict wind speeds for a real wind farm in the United States. The eight contrasting models are compared in terms of deterministic prediction and probabilistic prediction, respectively. The experimental results show that the LGB-GPR model improves the point forecast accuracy (RMSE) by up to 20.0% and improves the probabilistic forecast reliability (CRPS) by up to 21.5% compared to a single GPR model. This research is of great significance for improving the reliability of wind speed, probabilistic predictions, and the sustainable development of new energy.

Ensemble wind speed forecasting system based on optimal model adaptive selection strategy: Case study in China

Under the vision of global carbon neutrality and peaking, the vigorous development of easily accessible renewable energy sources, such as wind energy, is extremely important. However, achieving accurate and reliable forecasts remains a challenging problem owing to the irregularity and volatility of wind speed data. Existing forecasting modules based on point prediction ignore the limitations of a single forecasting algorithm, fail to capture the wind speed uncertainty in data or achieve high forecasting accuracy. To overcome these shortcomings, an ensemble system of decomposition, adaptive selection, and forecast was proposed to simulate the actual wind speed data of a wind farm. Empirical analyses show that an excellent denoising effect is achieved by the data decomposition method. Moreover, the adaptability of forecasting modules to complex data is improved by the optimal submodel selection strategy. The reduction coefficients are effectively optimized by the multi-objective bald eagle search algorithm used for the first time. This system not only improves the point forecasting accuracy but also analyzes the uncertainty of wind speed, providing actual technical support for grid dispatching.

Multi-population modelling and forecasting life-table death counts

When modelling the age distribution of death counts for multiple populations, we should consider three features: (1) how to incorporate any possible correlation among multiple populations to improve point and interval forecast accuracy through multi-population joint modelling; (2) how to forecast age distribution of death counts so that the forecasts are non-negative and have a constrained integral; (3) how to construct a prediction interval that is well-calibrated in terms of coverage. Within the framework of compositional data analysis, we apply a log-ratio transform to transform a constrained space into an unconstrained space. We apply multivariate and multilevel functional time series methods to forecast period life-table death counts in the unconstrained space. Through the inverse log-ratio transformation, the forecast period life-table death counts are obtained. Using the age-specific period life-table death counts in England and Wales and Sweden obtained from the Human Mortality Database (2022), we investigate one-step-ahead to 30-step-ahead point and interval forecast accuracies of the proposed models and make our recommendations.

Understanding the conditional out-of-sample predictive impact of the price of crude oil on aggregate equity return volatility

Using monthly data from 1973 through 2020, we explore whether it is possible to improve the accuracy of one-month ahead log-aggregate equity return realized volatility point forecasts by conditioning on various nonlinear crude oil price measures widely relied on in the literature. When evaluating the evidence of unconditional relative equal predictive ability as specified in Diebold and Mariano (1995), we observe that similar to well-known economic variables, such as the dividend yield, the default yield spread and the rate of inflation, we rarely observe evidence of statistical gains in relative point forecast accuracy in favor of the crude oil price-based models. However, when evaluating the evidence of conditionalrelative equal predictive ability as specified in Giacomini and White (2006), we observe that contrary to well-known economic predictors, certain nonlinear crude oil price variables, such as the one-year net crude oil price increase suggested in Hamilton (1996) offer sizable point forecast accuracy gains relative to the benchmark. These statistical gains can also be translated into economic gains.

Machine-Learning-Based Functional Time Series Forecasting: Application to Age-Specific Mortality Rates

We propose a functional time series method to obtain accurate multi-step-ahead forecasts for age-specific mortality rates. The dynamic functional principal component analysis method is used to decompose the mortality curves into dynamic functional principal components and their associated principal component scores. Machine-learning-based multi-step-ahead forecasting strategies, which automatically learn the underlying structure of the data, are used to obtain the future realization of the principal component scores. The forecasted mortality curves are obtained by combining the dynamic functional principal components and forecasted principal component scores. The point and interval forecast accuracy of the proposed method is evaluated using six age-specific mortality datasets and compared favorably with four existing functional time series methods.

An interesting finding about the ability of geopolitical risk to forecast aggregate equity return volatility out-of-sample

This study quantifies the relative predictive power afforded by the increasingly popular newspaper-based geopolitical risk (GPR) indices suggested in Caldara and Iacoviello (2018) with regards to forecasting aggregate equity return volatility out-of-sample. The central contribution of this short study to the mainstream equity return volatility predictability literature is to concisely demonstrate that when used as a regressor in the predictive model, the one-month lagged value of the logarithm of the GPR index of interest does not improve out-of-sample point forecast accuracy relative to the benchmark nor competitors employing well-known economic variables, such as the dividend yield, book-to-market ratio, default yield spread, the rate of inflation or the percentage change in the U.S. industrial production index. The same conclusion holds when the geopolitical risk indices are combined with these economic variables via simple point forecast combination schemes. However, the geopolitical risk indices are very useful in explaining the relative out-of-sample forecast performance of models employing certain economic variables and the benchmark. In fact, when the geopolitical risk indices are used as the “monitoring variable” under dynamic point forecast selection strategies, such as the one suggested in Zhu and Timmermann (2021), we are able to obtain sizable point forecast accuracy gains relative to the benchmark for certain economic variables.

An interpretable probabilistic model for short-term solar power forecasting using natural gradient boosting

PV power forecasting models are predominantly based on machine learning algorithms which do not provide any insight into or explanation about their predictions (black boxes). Therefore, their direct implementation in environments where transparency is required, and the trust associated with their predictions may be questioned. To this end, we propose a two stage probabilistic forecasting framework able to generate highly accurate, reliable, and sharp forecasts yet offering full transparency on both the point forecasts and the prediction intervals (PIs). In the first stage, we exploit natural gradient boosting (NGBoost) for yielding probabilistic forecasts, while in the second stage, we calculate the Shapley additive explanation (SHAP) values in order to fully comprehend why a prediction was made. To highlight the performance and the applicability of the proposed framework, real data from two PV parks located in Southern Germany are employed. Comparative results with two state-of-the-art algorithms, namely Gaussian process and lower upper bound estimation, manifest a significant increase in the point forecast accuracy and in the overall probabilistic performance. Most importantly, a detailed analysis of the model’s complex nonlinear relationships and interaction effects between the various features is presented. This allows interpreting the model, identifying some learned physical properties, explaining individual predictions, reducing the computational requirements for the training without jeopardizing the model accuracy, detecting possible bugs, and gaining trust in the model. Finally, we conclude that the model was able to develop complex nonlinear relationships which follow known physical properties as well as human logic and intuition.

Is the Group Structure Important in Grouped Functional Time Series?

We study the importance of group structure in grouped functional time series. Due to the non-uniqueness of group structure, we investigate different disaggregation structures in grouped functional time series. We address a practical question on whether or not the group structure can affect forecast accuracy. Using a dynamic multivariate functional time series method, we consider joint modeling and forecasting multiple series. Illustrated by Japanese sub-national age-specific mortality rates from 1975 to 2016, we investigate one- to 15-step-ahead point and interval forecast accuracies for the two group structures.