Optimal Forecast Combination Research Articles

An adaptive multi-objective optimal forecast combination and its application for predicting intermittent demand

While time series forecasting models are generally trained by optimising certain forms of error, the end-user’s forecasting needs in a multi-objective setting can be broader, and often mutually conflicting. A production manager may prioritise high product fill rates and low average inventory resulting from a forecast over just low error. The conflict among multiple objectives is notably worrisome in intermittent demand forecasting, where error-minimising approaches can devalue the practitioner’s objectives. To address such forecasting problems, we propose an Adaptive Multi-objective Optimal Combination (AMOC) of forecasts which incorporates the end-user’s preferences across multiple objectives. We demonstrate the use of AMOC in a real-life application of intermittent demand forecasting for optimising four distinct inventory management objectives using five specialised forecasting methods across single-period and multi-period inventory handling scenarios. Additionally, we conduct a comprehensive experiment on a subset of M5 competition data to exhibit the robustness of the AMOC using 13 diverse forecasting methods and four statistical objectives.

Optimal forecast combination based on PSO-CS approach for daily agricultural future prices forecasting

Forecasting agricultural commodity prices accurately is a challenging task due to the complexity of the trading market and the variability of influencing factors. Many studies have proven that forecast combination is an effective strategy for improving forecast performance relative to individual forecasting. In the field of forecast combination, how to determine the reasonable weights for combination is still an open question. This study proposed an optimal forecast combination framework for agricultural commodity prices forecasting, which integrates the decomposition–reconstruction–ensemble methodology with an improved nature-inspired global optimization algorithm. The update mechanism of particle swarm optimization (PSO) is introduced to improve cuckoo search (CS), in order to reduce the searching blindness in the huge exploration space. The framework consists of four steps. First, data decomposition using empirical wavelet transform (EWT), singular spectral analysis (SSA), and variational mode decomposition (VMD); Second, component reconstruction via a modified reconstruction approach based on the largest comprehensive grey correlation degree clustering (CGCD); Third, individual forecasting using autoregressive integrated moving average regression (ARIMA), exponential smoothing (ETS), back propagation neural network (BPNN) and extreme learning machine (ELM); Fourth, forecast combination via PSO-CS weight assignment method. Using corn and wheat future prices as research samples, the experimental results demonstrated that: (a) the PSO-CS weight assignment approach is superior to other combination approaches in most cases; (b) the CGCD approach can effectively reduce the computational cost of forecasting and improve the prediction performance; (c) the Full-PSO-CS model provides the most accurate forecast due to the diversity of individual forecasts, it reduces MAPE by 43.66% and improves directional accuracy by 30.80% on average compared with the best single model.

Climate Services Toolbox (CSTools) v4.0: from climate forecasts to climate forecast information

Abstract. Despite the wealth of existing climate forecast data, only a small part is effectively exploited for sectoral applications. A major cause of this is the lack of integrated tools that allow the translation of data into useful and skillful climate information. This barrier is addressed through the development of an R package. Climate Services Toolbox (CSTools) is an easy-to-use toolbox designed and built to assess and improve the quality of climate forecasts for seasonal to multi-annual scales. The package contains process-based, state-of-the-art methods for forecast calibration, bias correction, statistical and stochastic downscaling, optimal forecast combination, and multivariate verification, as well as basic and advanced tools to obtain tailored products. Due to the modular design of the toolbox in individual functions, the users can develop their own post-processing chain of functions, as shown in the use cases presented in this paper, including the analysis of an extreme wind speed event, the generation of seasonal forecasts of snow depth based on the SNOWPACK model, and the post-processing of temperature and precipitation data to be used as input in impact models.

Bayesian forecast combination using time-varying features

In this work, we propose a novel framework for density forecast combination by constructing time-varying weights based on time-varying features. Our framework estimates weights in the forecast combination via Bayesian log predictive scores, in which the optimal forecast combination is determined by time series features from historical information. In particular, we use an automatic Bayesian variable selection method to identify the importance of different features. To this end, our approach has better interpretability compared to other black-box forecasting combination schemes. We apply our framework to stock market data and M3 competition data. Based on our structure, a simple maximum-a-posteriori scheme outperforms benchmark methods, and Bayesian variable selection can further enhance the accuracy for both point forecasts and density forecasts.

Using polls to forecast popular vote share for US presidential elections 2016 and 2020: An optimal forecast combination based on ensemble empirical model

This study introduces the Ensemble Empirical Mode Decomposition (EEMD) technique to forecasting popular vote shares in general elections. The technique is useful when using polling data. Our main interest in this study is shorter- and longer-term forecasting and, thus, we consider from the shortest forecast horizon of 1-day to three months ahead. The EEMD technique is used to decompose the election data for the two most recent US presidential elections; 2016 and 2020. Three models, Support Vector Machine (SVM), Neural Network (NN) and ARIMA models are then used to predict the decomposition components. Subsequently, the final hybrid model is constructed by comparing the prediction performance of the decomposition components. The predicting performance of the combination model is compared with the benchmark individual models: SVM, NN, and ARIMA. Finally, this is also compared to the single prediction market IOWA Electronic Markets. The results indicate that the prediction performance of combined EEMD model is better than that of the individual models.

Optimal Forecast Combination Based on Pso-Cs Approach for Daily Agricultural Future Prices Forecasting

Optimal Forecast Combination Based on Pso-Cs Approach for Daily Agricultural Future Prices Forecasting

Optimal forecast combination based on ensemble empirical mode decomposition for agricultural commodity futures prices

AbstractImproving the prediction accuracy of agricultural product futures prices is important for investors, agricultural producers, and policymakers. This is to evade risks and enable government departments to formulate appropriate agricultural regulations and policies. This study employs the ensemble empirical mode decomposition (EEMD) technique to decompose six different categories of agricultural futures prices. Subsequently, three models—support vector machine (SVM), neural network (NN), and autoregressive integrated moving average (ARIMA)—are used to predict the decomposition components. The final hybrid model is then constructed by comparing the prediction performance of the decomposition components. The predicting performance of the combination model is then compared with the benchmark individual models: SVM, NN, and ARIMA. Our main interest in this study is on short‐term forecasting, and thus we only consider 1‐day and 3‐day forecast horizons. The results indicate that the prediction performance of the EEMD combined model is better than that of individual models, especially for the 3‐day forecasting horizon. The study also concluded that the machine learning methods outperform the statistical methods in forecasting high‐frequency volatile components. However, there is no obvious difference between individual models in predicting low‐frequency components.

Robust optimization of forecast combinations

We develop a methodology for constructing robust combinations of time series forecast models which improve upon a given benchmark specification for all symmetric and convex loss functions. Under standard regularity conditions, the optimal forecast combination asymptotically almost surely dominates the benchmark, and also optimizes the chosen goal function. The optimum in a given sample can be found by solving a convex optimization problem. An application to the forecasting of changes in the S&P 500 volatility index shows that robust optimized combinations improve significantly upon the out-of-sample forecasting accuracy of both simple averaging and unrestricted optimization.

Optimal Forecast Combination Based on Neural Networks for Time Series Forecasting

Research indicates that forecast combination is one of the most important and effective approaches for time series forecasting. The success of forecast combination depends on how well component models are selected and combination weights are determined. A forecast combination model resulting from a new neural networks-based linear ensemble framework (NNsLEF) is proposed in this study. The principle of the proposed framework adheres to three primary aspects. (a) Four kinds of neural network models, namely, back-propagation neural network, dynamic architecture for artificial neural network, Elman artificial neural network, and echo state network, are selected as component forecasting models. (b) An input-hidden selection heuristic (IHSH) is designed to determine the input-hidden neuron combination for each component neural network. (c) An in-sample training–validation pair-based neural network weighting (ITVPNNW) mechanism is studied to generate the associated combination weights. In particular, the four neural network models are applied to impart their superior performance to the combination approach while maintaining their diversity. Meanwhile, IHSH is investigated to improve the performance of each component neural network model by attempting to solve the familiar overfitting problem of networks. Lastly, the ITVPNNW mechanism is studied to search for a set of appropriate combination weights that will primarily affect the accuracy of the linear ensemble framework. Resultsfrom experiments performed on eight time series data sets show that NNsLEF outperforms the four component neural network models and other well-recognized models.

Robust Optimization of Forecast Combinations

A methodology is developed for constructing robust forecast combinations which improve upon a given benchmark specification for all symmetric and convex loss functions. The optimal forecast combination asymptotically almost surely dominates the benchmark and, in addition, minimizes the expected loss function, under standard regularity conditions. The optimum in a given sample can be found by solving a large Convex Optimization problem. An application to forecasting of changes of the S&P 500 Volatility Index shows that robust optimized combinations improve significantly upon the out-of-sample forecasting accuracy of simple averaging and unrestricted optimization.

Quantile forecast combination using stochastic dominance

This paper derives optimal forecast combinations based on stochastic dominance efficiency (SDE) analysis with differential forecast weights for different quantiles of forecast error distribution. For the optimal forecast combination, SDE will minimize the cumulative density functions of the levels of loss at different quantiles of the forecast error distribution by combining different time-series model-based forecasts. Using two exchange rate series on weekly data for the Japanese yen/US dollar and US dollar/Great Britain pound, we find that the optimal forecast combinations with SDE weights perform better than different forecast selection and combination methods for the majority of the cases at different quantiles of the error distribution. However, there are also some very few cases where some other forecast selection and combination model performs equally well at some quantiles of the forecast error distribution. Different forecasting period and quadratic loss function are used to obtain optimal forecast combinations, and results are robust to these choices. The out-of-sample performance of the SDE forecast combinations is also better than that of the other forecast selection and combination models we considered.

How do I know if I’ve improved my continental scale flood early warning system?

Flood early warning systems mitigate damages and loss of life and are an economically efficient way of enhancing disaster resilience. The use of continental scale flood early warning systems is rapidly growing. The European Flood Awareness System (EFAS) is a pan-European flood early warning system forced by a multi-model ensemble of numerical weather predictions. Responses to scientific and technical changes can be complex in these computationally expensive continental scale systems, and improvements need to be tested by evaluating runs of the whole system. It is demonstrated here that forecast skill is not correlated with the value of warnings. In order to tell if the system has been improved an evaluation strategy is required that considers both forecast skill and warning value.The combination of a multi-forcing ensemble of EFAS flood forecasts is evaluated with a new skill-value strategy. The full multi-forcing ensemble is recommended for operational forecasting, but, there are spatial variations in the optimal forecast combination. Results indicate that optimizing forecasts based on value rather than skill alters the optimal forcing combination and the forecast performance. Also indicated is that model diversity and ensemble size are both important in achieving best overall performance. The use of several evaluation measures that consider both skill and value is strongly recommended when considering improvements to early warning systems.

Is there an optimal forecast combination?

We consider several geometric approaches for combining forecasts in large samples—a simple eigenvector approach, a mean corrected eigenvector and trimmed eigenvector approach. We give conditions where geometric approach yields identical result as the regression approach. We also consider a mean and scale corrected simple average of all predictive models for finite sample and give conditions where simple average is an optimal combination. Monte Carlos are conducted to compare the finite sample performance of these and some popular forecast combination and information combination methods and to shed light on the issues of “forecast combination” vs “information combination”. We also try to shed light on whether there exists an optimal forecast combination method by comparing various forecast combination methods to predict US real output growth rate and excess equity premium.

More on stochastic index numbers

There are three major approaches used to estimate index numbers. The first is Fisher's test approach whereby indexes are judged on their ability to satisfy certain criteria. The economic theory of index numbers is the second approach and this deals with their foundations in utility theory. The third approach is a less well-known methodology, but one which is now attracting considerable attention, the stochastic approach which is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. While providing a point estimate for the index number like the other two approaches, the stochastic approach additionally provides the SE of the point estimate. This article enhances understanding of stochastic index numbers by showing that they are formally equivalent to the familiar optimal combination of forecasts with the individual prices playing the role of n forecasts of the overall rate of inflation. This leads to new analytical results on the impact of adding additional information within the stochastic approach framework. We provide two concrete examples of the sources of such additional information: (i) the quantity theory of money; and (ii) the use of quantity data in addition to price data. We also illustrate some of these theoretical results using real data.

Some Implications of a Quartic Loss Function

Motivated by a central banker with a symmetric inflation zone target, we assume in this letter that the loss function of a policy maker can be approximated by the quartic form. For non-normal distributions, we show that such a loss function implies a systematic inflation bias even when the bank targets the natural rate. Moreover, we illustrate that the weights in an optimal combination of forecasts will differ from that under quadratic loss. We illustrate these differences via simulated data and data from the Livingston Surveys of Professional Forecasters.

Persistence in forecasting performance and conditional combination strategies

This paper considers measures of persistence in the (relative) forecasting performance of linear and nonlinear time-series models applied to a large cross-section of economic variables in the G7 countries. We find strong evidence of persistence among top and bottom forecasting models and relate this to the possibility of improving performance through forecast combinations. We propose a new four-stage conditional model combination method that first sorts models into clusters based on their past performance, then pools forecasts within each cluster, followed by estimation of the optimal forecast combination weights for these clusters and shrinkage towards equal weights. These methods are shown to work well empirically in out-of-sample forecasting experiments.

Optimal forecast combinations under general loss functions and forecast error distributions

Existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss. Under this loss function empirical studies have generally found that equally-weighted combined forecasts lead to better performance than estimates of optimal forecast combination weights which in turn outperform the best individual predictions. We show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed. We characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights. We also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise.

Optimal Forecast Combinations Under General Loss Functions and Forecast Error Distributions

Existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss. Under this loss function empirical studies have generally found that estimates of optimal forecast combination weights lead to higher losses than equally-weighted combined forecasts which in turn outperform the best individual predictions. We show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed. We characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights. We also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise.

Efficient forecasting in nearly non-stationary processes

This paper proposes a procedure to make efficient predictions in a nearly non-stationary process. The method is based on the adaptation of the theory of optimal combination of forecasts to nearly non-stationary processes. The proposed combination method is simple to apply and has a better performance than classical combination procedures. It also has better average performance than a differenced predictor, a fractional differenced predictor, or an optimal unit-root pretest predictor. In the case of a process that has a zero mean, only the non-differenced predictor is slightly better than the proposed combination method. In the general case of a non-zero mean, the proposed combination method has a better overall performance than all its competitors. Copyright © 2002 John Wiley & Sons, Ltd.

Efficient forecasting in nearly non‐stationary processes

AbstractThis paper proposes a procedure to make efficient predictions in a nearly non‐stationary process. The method is based on the adaptation of the theory of optimal combination of forecasts to nearly non‐stationary processes. The proposed combination method is simple to apply and has a better performance than classical combination procedures. It also has better average performance than a differenced predictor, a fractional differenced predictor, or an optimal unit‐root pretest predictor. In the case of a process that has a zero mean, only the non‐differenced predictor is slightly better than the proposed combination method. In the general case of a non‐zero mean, the proposed combination method has a better overall performance than all its competitors. Copyright © 2002 John Wiley & Sons, Ltd.