Combined Forecasting Method Research Articles

Optimal Selection of Expert Forecasts with Integer Programming

Combinations of point forecasts from expert forecasters are known to frequently outperform individual forecasts. It is also well documented that combination by simple averaging very often has performance superior to that of more sophisticated combinations. This empirical fact is referred to as the ‘forecast combination puzzle’ in the literature. In this paper, we propose a combination method that exploits this puzzle. Rather than averaging over all forecasts, our method optimally selects forecasts for averaging. The problem of optimal selection is solved using integer programming, a solution approach that has witnessed astonishing advancements. We apply this new method to forecasts of real GDP growth and unemployment from the European Central Bank Survey of Professional Forecasters. The results show that it is optimal to select only a small number of the available forecasts and that averaging over these small subsets almost always provides performance that is superior to averaging over all forecasts. Importantly, this new method is consistently one of the best performers when evaluated against a wide range of alternative forecast combination methods.

A new consensus between the mean and median combination methods to improve forecasting accuracy

To improve the forecasting accuracies, researchers have long been using various combination techniques. In particular, the use of dissimilar methods for forecasting time series data is expected to provide superior results. Although numerous combination techniques have been proposed until date, the simple combination techniques - such as mean and median - maintain their strength, popularity, and utility. This paper proposes a new combination method based on the mean and median combination methods so as to combine the advantages of both these methods. The proposed combination technique attempts to utilize the strong aspects of each method and minimize the risk that arises from the selection of the combination method with poor performance. In order to depict the potential power of the proposed combining method, well-known six real-world time series data were used. Our results indicate that the proposed method presents with promising performances. In addition, a nonparametric statistical test was exploited to reveal the superiority of the proposed method over the single methods and other forecast combination methods from all of the investigated data sets.

Forecast Combination for Euro Area Inflation - A Cure in Times of Crisis?

The period of extraordinary volatility in euro area headline inflation starting in 2007 raised the question whether forecast combination methods can be used to hedge against bad forecast performance of single models during such periods and provide more robust forecasts. We investigate this issue for forecasts from a range of short-term forecasting models. Our analysis shows that there is considerable variation of the relative performance of the different models over time. To take that into account we suggest employing performance-based forecast combination methods, in particular one with more weight on the recent forecast performance. We compare such an approach with equal forecast combination that has been found to outperform more sophisticated forecast combination methods in the past, and investigate whether it can improve forecast accuracy over the single best model. The time-varying weights assign weights to the economic interpretations of the forecast stemming from different models. The combination methods are evaluated for HICP headline inflation and HICP excluding food and energy. We investigate how forecast accuracy of the combination methods differs between pre-crisis times, the period after the global financial crisis and the full evaluation period including the global financial crisis with its extraordinary volatility in inflation. Overall, we find that, first, forecast combination helps hedge against bad forecast performance and, second, that performance-based weighting tends to outperform simple averaging.

Output Prediction of Photovoltaic Power Station Based on Nonlinear Combined Model

The output prediction of photovoltaic (PV) power station is necessary because the weather, environment and seasonal factors lead to the unstable PV power generation, which will affect the planning and scheduling of power system. Compared with the single model method, the linear combination method could improve the prediction accuracy of the output of PV power station. However, the linear combination forecast method is a simple convex combination of different prediction methods and is lack of general applicability. This paper presents a nonlinear combination method based on BP neural network and ARMA model to predict the output of PV power plant. This method based on the nonlinear relationship between the results of two single prediction models and the actual value, and utilize the nonlinear fitting ability of BP neural network, predicted the power generation capacity of PV power station. The nonlinear prediction theory and algorithm are given at the end of the article, and also compare nonlinear combined model with linear combined model of the power plant output prediction, the results show that the proposed method has a high accuration and an extensive applicability.

Forecasting city arrivals with Google Analytics

The ability of 10 Google Analytics website traffic indicators from the Viennese DMO website to predict actual tourist arrivals to Vienna is investigated within the VAR model class. To prevent overparameterization, big data shrinkage methods are applied: Bayesian estimation of the VAR, reduction to a factor-augmented VAR, and application of Bayesian estimation to the FAVAR, the novel Bayesian FAVAR. Forecast accuracy results show that for shorter horizons (h=1, 2months ahead) a univariate benchmark performs best, while for longer horizons (h=3, 6, 12) forecast combination methods that include the predictive information of Google Analytics perform best, notably combined forecasts based on Bates–Granger weights, on forecast encompassing tests, and on a novel fusion of these two.

Forecasting market returns: bagging or combining?

This paper provides a rigorous and detailed analysis of bagging methods, which address both model and parameter uncertainty. We provide a multi-country study of bagging, of which there have been very few to date, that examines out-of-sample forecasts for the G7 and a broad set of Asian countries. We find that bagging generally improves the forecast accuracy and generates economic gains relative to the benchmark when portfolio weight restrictions are applied. Bagging also performs well compared to forecast combinations in this setting. We incorporate data mining critical values for appropriate inference on bagging and combination forecast methods. We provide new evidence that the results for bagging cannot be explained fully by data mining concerns. Finally, the forecasting gains are highest for countries with high trade openness and high FDI. The potentially substantial economic gains could well be operational, given the existence of index funds for most of these countries.

Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods

A number of recent studies in the economics literature have focused on the usefulness of factor models in the context of prediction using “big data” (see Bai and Ng, 2008; Dufour and Stevanovic, 2010; Forni, Hallin, Lippi, & Reichlin, 2000; Forni et al., 2005; Kim and Swanson, 2014a; Stock and Watson, 2002b, 2006, 2012, and the references cited therein). We add to this literature by analyzing whether “big data” are useful for modelling low frequency macroeconomic variables, such as unemployment, inflation and GDP. In particular, we analyze the predictive benefits associated with the use of principal component analysis (PCA), independent component analysis (ICA), and sparse principal component analysis (SPCA). We also evaluate machine learning, variable selection and shrinkage methods, including bagging, boosting, ridge regression, least angle regression, the elastic net, and the non-negative garotte. Our approach is to carry out a forecasting “horse-race” using prediction models that are constructed based on a variety of model specification approaches, factor estimation methods, and data windowing methods, in the context of predicting 11 macroeconomic variables that are relevant to monetary policy assessment. In many instances, we find that various of our benchmark models, including autoregressive (AR) models, AR models with exogenous variables, and (Bayesian) model averaging, do not dominate specifications based on factor-type dimension reduction combined with various machine learning, variable selection, and shrinkage methods (called “combination” models). We find that forecast combination methods are mean square forecast error (MSFE) “best” for only three variables out of 11 for a forecast horizon of h=1, and for four variables when h=3 or 12. In addition, non-PCA type factor estimation methods yield MSFE-best predictions for nine variables out of 11 for h=1, although PCA dominates at longer horizons. Interestingly, we also find evidence of the usefulness of combination models for approximately half of our variables when h>1. Most importantly, we present strong new evidence of the usefulness of factor-based dimension reduction when utilizing “big data” for macroeconometric forecasting.

Housing Value Estimation: An Application of Forecast Combination to Residential Property Valuation

In this study we use property-level transaction data to construct several different out-of-sample forecasts for the sales of individual homes in 10 counties in Florida. We utilize a number of common forecast combination methods and analyze the properties of their forecast errors. The results from this analysis suggest that relatively simple forecast combination schemes have the potential to reduce the error in property value estimates, possibly by a wide margin. Lastly, we find that the forecast error associated with constructing valuations using popular house price indices has been very large in our sample.

The Dog Has Barked for a Long Time: Dividend Growth Is Predictable

The Campbell-Shiller present value identity implies that (i) the dividend-price ratio should forecast returns or dividend growth, and (ii) any other predictor of returns should also forecast dividend growth, and vice versa. Prior literature investigates (i) and finds that dividend growth appears unpredictable based on forecasting regressions with the dividend-price ratio. We investigate (ii) and combine out-of-sample dividend-growth forecasts from 14 individual predictive regressions based on common return predictors. Encompassing and structural break tests show these individual return predictors contribute disparate and unstable univariate forecasts of dividend growth. Combination forecast methods of 14 common return predictors overcome these econometric problems and generate robust out-of sample predictability of dividend growth over the entire post-war period as well as over most sub-periods. The dividend-growth forecasts coupled with the dividend-price ratio also significantly forecast excess returns out-of-sample.

Mining Big Data Using Parsimonious Factor, Machine Learning, Variable Selection and Shrinkage Methods

A number of recent studies in the economics literature have focused on the usefulness of factor models in the context of prediction using big data. We add to this literature by analyzing whether big are useful for modelling low frequency macroeconomic variables such as unemployment, inflation and GDP. In particular, we analyze the predictive benefits associated with the use of principal component analysis (PCA), independent component analysis (ICA), and sparse principal component analysis (SPCA). We also evaluate machine learning, variable selection and shrinkage methods, including bagging, boosting, ridge regression, least angle regression, the elastic net, and the non-negative garotte. Our approach is to carry out a forecasting horse-race using prediction models constructed using a variety of model specification approaches, factor estimation methods, and data windowing methods, in the context of the prediction of 11 macroeconomic variables relevant for monetary policy assessment. In many instances, we find that various of our benchmark models, including autoregressive (AR) models, AR models with exogenous variables, and (Bayesian) model averaging, do not dominate specifications based on factor-type dimension reduction combined with various machine learning, variable selection, and shrinkage methods (called models). We find that forecast combination methods are mean square forecast error (MSFE) best for only 3 of 11 variables when the forecast horizon, h=1, and for 4 variables when h=3 or 12. Additionally, non-PCA type factor estimation methods yield MSFE-best predictions for 9 of 11 variables when h=1, although PCA dominates at longer horizons. Interestingly, we also find evidence of the usefulness of combination models for approximately 1/2 of our variables, when h>1. Most importantly, we present strong new evidence of the usefulness of factor based dimension reduction, when utilizing big for macroeconometric forecasting.

Modelization of the Current and Future Habitat Suitability of Rhododendron ferrugineum Using Potential Snow Accumulation.

Mountain areas are particularly sensitive to climate change. Species distribution models predict important extinctions in these areas whose magnitude will depend on a number of different factors. Here we examine the possible impact of climate change on the Rhododendron ferrugineum (alpenrose) niche in Andorra (Pyrenees). This species currently occupies 14.6 km2 of this country and relies on the protection afforded by snow cover in winter. We used high-resolution climatic data, potential snow accumulation and a combined forecasting method to obtain the realized niche model of this species. Subsequently, we used data from the high-resolution Scampei project climate change projection for the A2, A1B and B1 scenarios to model its future realized niche model. The modelization performed well when predicting the species’s distribution, which improved when we considered the potential snow accumulation, the most important variable influencing its distribution. We thus obtained a potential extent of about 70.7 km2 or 15.1% of the country. We observed an elevation lag distribution between the current and potential distribution of the species, probably due to its slow colonization rate and the small-scale survey of seedlings. Under the three climatic scenarios, the realized niche model of the species will be reduced by 37.9–70.1 km2 by the end of the century and it will become confined to what are today screes and rocky hillside habitats. The particular effects of climate change on seedling establishment, as well as on the species’ plasticity and sensitivity in the event of a reduction of the snow cover, could worsen these predictions.

Forecast Combination for Euro Area Inflation: A Cure in Times of Crisis?

The period of extraordinary volatility in euro area headline inflation starting in 2007 raised the question whether forecast combination methods can be used to hedge against bad forecast performance of single models during such periods and provide more robust forecasts. We investigate this issue for forecasts from a range of short-term forecasting models. Our analysis shows that there is considerable variation of the relative performance of the different models over time. To take that into account we suggest employing performance-based forecast combination methods, in particular one with more weight on the recent forecast performance. We compare such an approach with equal forecast combination that has been found to outperform more sophisticated forecast combination methods in the past, and investigate whether it can improve forecast accuracy over the single best model. The time-varying weights assign weights to the economic interpretations of the forecast stemming from different models. We also include a number of benchmark models in our analysis. The combination methods are evaluated for HICP headline inflation and HICP excluding food and energy. We investigate how forecast accuracy of the combination methods differs between pre-crisis times, the period after the global financial crisis and the full evaluation period including the global financial crisis with its extraordinary volatility in inflation. Overall, we find that forecast combination helps hedge against bad forecast performance and that performance-based weighting outperforms simple averaging. JEL Classification: C32, C52, C53, E31, E37

A Novel Combination Forecast Method on Non-Stationary Time Series and Its Application to Exchange Rate Forecasting

A Novel Combination Forecast Method on Non-Stationary Time Series and Its Application to Exchange Rate Forecasting

基于LASSO-SVM模型的银行定期存款电话营销预测

定期存款一直以来都是银行的主要资金来源，而电话营销也成为一种低成本，广受银行欢迎的营销模式。因此，如何提高电话营销成功率成为银行急需解决的重要问题。其中，影响客户订购定期存款的因素复杂多样，而这些因素之间可能存在多重共线性，如果银行不加选择地引入众多影响因素来进行订购定期存款的预测，往往不能取得良好的预测效果，甚至产生错误的决策。在统计学习方法中，LASSO方法可以同时进行参数估计和变量选择，所以本文提出了基于LASSO与支持向量机的组合预测方法。同时，与SVM、神经网络、LASSO-神经网络方法的预测效果进行比较，验证了LASSO-支持向量机组合预测方法的拟合预测效果要优于另外三种预测方法。 Time deposits have always been the main source of funds for the bank, and the telephone mar-keting has become a low-cost marketing model, which is widely popular with the bank. Therefore, how to improve the success rate of telemarketing has become an important problem to solve. Among them, the factors that affect customers ordering deposits are complicated, which may have multicollinearity. If banks indiscriminately use many influence factors to predict deposits, they often cannot obtain good prediction effects, and even make the wrong decision. In the statistical learning methods, the LASSO method can be used to estimate parameters and select variables, so this paper presents a combination forecast method based on the LASSO and Support Vector Ma-chine (SVM). At the same time, compared with SVM, neural network, LASSO-neural network me-thods, we find that the effect of LASSO-SVM forecasting method is better than the other three kinds of forecasting methods.

A Robust Weighted Combination Forecasting Method Based on Forecast Model Filtering and Adaptive Variable Weight Determination

Medium-and-long-term load forecasting plays an important role in energy policy implementation and electric department investment decision. Aiming to improve the robustness and accuracy of annual electric load forecasting, a robust weighted combination load forecasting method based on forecast model filtering and adaptive variable weight determination is proposed. Similar years of selection is carried out based on the similarity between the history year and the forecast year. The forecast models are filtered to select the better ones according to their comprehensive validity degrees. To determine the adaptive variable weight of the selected forecast models, the disturbance variable is introduced into Immune Algorithm-Particle Swarm Optimization (IA-PSO) and the adaptive adjustable strategy of particle search speed is established. Based on the forecast model weight determined by improved IA-PSO, the weighted combination forecast of annual electric load is obtained. The given case study illustrates the correctness and feasibility of the proposed method.

Robustness of Forecast Combination in Unstable Environment: A Monte Carlo Study of Advanced Algorithms

Based on a set of carefully designed Monte Carlo exercises, this paper documents the behavior and performance of several newly developed advanced forecast combination algorithms in unstable environments, where performance of candidate forecasts are cross-sectionally heterogeneous and dynamically evolving over time. Results from these exercises provide guidelines regarding the selection of forecast combination method based on the nature, frequency, and magnitude of instabilities in forecasts as well as the target variable. Following these guidelines, a simple forecast combination procedure is proposed and demonstrated through a real-time forecast combination exercise using the U.S. Survey of Professional Forecasters, where combined forecasts are shown to have superior performance that is not only statistically significant but also of practical importance.

Forecast Combination under Heavy-Tailed Errors

Forecast combination has been proven to be a very important technique to obtain accurate predictions for various applications in economics, finance, marketing and many other areas. In many applications, forecast errors exhibit heavy-tailed behaviors for various reasons. Unfortunately, to our knowledge, little has been done to obtain reliable forecast combinations for such situations. The familiar forecast combination methods, such as simple average, least squares regression or those based on the variance-covariance of the forecasts, may perform very poorly due to the fact that outliers tend to occur, and they make these methods have unstable weights, leading to un-robust forecasts. To address this problem, in this paper, we propose two nonparametric forecast combination methods. One is specially proposed for the situations in which the forecast errors are strongly believed to have heavy tails that can be modeled by a scaled Student’s t-distribution; the other is designed for relatively more general situations when there is a lack of strong or consistent evidence on the tail behaviors of the forecast errors due to a shortage of data and/or an evolving data-generating process. Adaptive risk bounds of both methods are developed. They show that the resulting combined forecasts yield near optimal mean forecast errors relative to the candidate forecasts. Simulations and a real example demonstrate their superior performance in that they indeed tend to have significantly smaller prediction errors than the previous combination methods in the presence of forecast outliers.

Out-of-Sample Equity Premium Predictability in South Africa: Evidence from a Large Number of Predictors

ABSTRACTThis article uses a predictive regression framework to examine the out-of-sample predictability of South Africa’s equity premium, using a host of financial and macroeconomic variables. We employ various methods of forecast combination, bootstrap aggregation (bagging), diffusion index (principal component), and Bayesian regressions to allow for a simultaneous role of the variables under consideration, besides individual predictive regressions. We assess both the statistical and economic significance of the individual predictive regressions, combination methods, bagging, principal components, and Bayesian regressions. Our results show that forecast combination methods and principal component regressions improve the predictability of the equity premium relative to the benchmark autoregressive model of order one (AR[1]). However, the Bayesian predictive regressions are found to be the standout performers with the models outperforming the individual regressions, forecast combination methods, bagging and principal component regressions, both in terms of statistical (forecasting) and economic (utility) gains.

Coupling Forecast Methods of Multiple Rainfall–Runoff Models for Improving the Precision of Hydrological Forecasting

With much more higher requirement for the precision of flood forecasting and length of forecast period in the hydrological operational predication, three coupling forecast methods which include real-time correction—combination forecast (RC-CF) method, combination forecast—real-time correction (CF-RC) method, and Integral Parameters Optimization (IPO) method are proposed in this paper for the purpose of improving the precision of flood forecasting. These coupling forecast methods are based on the real-time correction and combination forecast methods. Thereafter, two methods (method A & method B) are proposed for the purpose of prolonging the forecast period. Furthermore, indices of accuracy assessment which consist of mean absolute error, mean relative error, certainty coefficient and root-mean-square error are utilized to evaluate the forecast results of coupling forecast methods. Moreover, with a case study of Xiangjiaba station in the Jinsha River, advantages and disadvantages of these coupling forecast methods are obtained through the comparison of forecast results calculated by these methods, and they provide the basis for selection of coupling forecast methods. The result shows that the IPO method performs better than other two methods which behave undifferentiated. It is found that the IPO method combined with method B can be a viable alternative for flood forecasting of multiple hydrological models.

Structural-break models under mis-specification: Implications for forecasting

This paper revisits the least squares estimator of the linear regression with a structural break. We view the model as an approximation to the true data generating process whose exact nature is unknown but perhaps changing over time either continuously or with some jumps. This view is widely held in the forecasting literature and under this view, the time series dependence property of all the observed variables is unstable as well. We establish that the rate of convergence of the estimator to a properly defined limit is at most the cube root of T, where T is the sample size, which is much slower than the standard super consistent rate. We also provide an asymptotic distribution of the estimator and that of the Gaussian quasi likelihood ratio statistic for a certain class of true data generating processes. We relate our finding to current forecast combination methods and propose a new averaging scheme. Our method compares favourably with various contemporary forecasting methods in forecasting a number of macroeconomic series.