Linear transformations of vector ARMA processes

Linear transformations of stochastic processes are used in many ways in economic analyses, for example when linear aggregates or subprocesses are considered. It is demonstrated that a linear transformation of a vector ARMA process is again an ARMA process and conditions for stationarity are given. Three different predictors for a linearly transformed process are compared. Forecasting the original process and transforming the predictions is superior to forecasting the transformed process directly and to transforming univariate predictions of the components of the original process. Conditions for equality of the three different forecasts are provided.     

Macroeconomic forecasting for Australia using a large number of predictors

A popular approach to forecasting macroeconomic variables is to utilize a large number of predictors. Several regularization and shrinkage methods can be used to exploit such high-dimensional datasets, and have been shown to improve forecast accuracy for the US economy. To assess whether similar results hold for economies with different characteristics, an Australian dataset containing observations on 151 aggregate and disaggregate economic series as well as 185 international variables, is introduced. An extensive empirical study is carried out investigating forecasts at different horizons, using a variety of methods and with information sets containing an increasing number of predictors. In contrast to other countries the results show that it is difficult to forecast Australian key macroeconomic variables more accurately than some simple benchmarks. In line with other studies we also find that there is little to no improvement in forecast accuracy when the number of predictors is expanded beyond 20–40 variables and international factors do not seem to help.     

Evaluating predictive densities of US output growth and inflation in a large macroeconomic data set

We evaluate conditional predictive densities for US output growth and inflation using a number of commonly-used forecasting models that rely on large numbers of macroeconomic predictors. More specifically, we evaluate how well conditional predictive densities based on the commonly-used normality assumption fit actual realizations out-of-sample. Our focus on predictive densities acknowledges the possibility that, although some predictors can cause point forecasts to either improve or deteriorate, they might have the opposite effect on higher moments. We find that normality is rejected for most models in some dimension according to at least one of the tests we use. Interestingly, however, combinations of predictive densities appear to be approximated correctly by a normal density: the simple, equal average when predicting output growth, and the Bayesian model average when predicting inflation.     

Forecasting inflation using time‐varying Bayesian model averaging

This paper presents a Bayesian model averaging regression framework for forecasting US inflation, in which the set of predictors included in the model is automatically selected from a large pool of potential predictors and the set of regressors is allowed to change over time. Using real‐time data on the 1960–2011 period, this model is applied to forecast personal consumption expenditures and gross domestic product deflator inflation. The results of this forecasting exercise show that, although it is not able to beat a simple random‐walk model in terms of point forecasts, it does produce superior density forecasts compared with a range of alternative forecasting models. Moreover, a sensitivity analysis shows that the forecasting results are relatively insensitive to prior choices and the forecasting performance is not affected by the inclusion of a very large set of potential predictors.     

The M4 Competition: Results,findings, conclusion and way forward

The M4 competition is the continuation of three previous competitions started more than 45 years ago whose purpose was to learn how to improve forecasting accuracy, and how such learning can be applied to advance the theory and practice of forecasting. The purpose of M4 was to replicate the results of the previous ones and extend them into three directions: First significantly increase the number of series, second include Machine Learning (ML) forecasting methods, and third evaluate both point forecasts and prediction intervals. The five major findings of the M4 Competitions are: 1. Out Of the 17 most accurate methods, 12 were “combinations” of mostly statistical approaches. 2. The biggest surprise was a “hybrid” approach that utilized both statistical and ML features. This method’s average sMAPE was close to 10% more accurate than the combination benchmark used to compare the submitted methods. 3. The second most accurate method was a combination of seven statistical methods and one ML one, with the weights for the averaging being calculated by a ML algorithm that was trained to minimize the forecasting. 4. The two most accurate methods also achieved an amazing success in specifying the 95% prediction intervals correctly. 5. The six pure ML methods performed poorly, with none of them being more accurate than the combination benchmark and only one being more accurate than Naïve2. This paper presents some initial results of M4, its major findings and a logical conclusion. Finally, it outlines what the authors consider to be the way forward for the field of forecasting.     

Optimal error and GMDH predictors: A comparison with some statistical techniques

This paper presents some results obtained in time series forecasting using two nonstandard approaches and compares them with those obtained by usual statistical techniques. In particular, a new method based on recent results of the General Theory of Optimal Algorithm is considered. This method may be useful when no reliable statistical hypotheses can be made or when a limited number of observations is available. Moreover, a nonlinear modelling technique based on Group Method of Data Handling (GMDH) is also considered to derive forecasts. The well-known Wolf Sunspot Numbers and Annual Canadian Lynx Trappings series are analyzed; the Optimal Error Predictor is also applied to a recently published demographic series on Australian Births. The reported results show that the Optimal Error and GMDH predictors provide accurate one step ahead forecasts with respect to those obtained by some linear and nonlinear statistical models. Furthermore, the Optimal Error Predictor shows very good performances in multistep forecasting.     

Criteria for classifying forecasting methods

Classifying forecasting methods as being either of a “machine learning” or “statistical” nature has become commonplace in parts of the forecasting literature and community, as exemplified by the M4 competition and the conclusion drawn by the organizers. We argue that this distinction does not stem from fundamental differences in the methods assigned to either class. Instead, this distinction is probably of a tribal nature, which limits the insights into the appropriateness and effectiveness of different forecasting methods. We provide alternative characteristics of forecasting methods which, in our view, allow to draw meaningful conclusions. Further, we discuss areas of forecasting which could benefit most from cross-pollination between the ML and the statistics communities.     

Understanding machine learning-based forecasting methods: A decomposition framework and research opportunities

Machine learning (ML) methods are gaining popularity in the forecasting field, as they have shown strong empirical performance in the recent M4 and M5 competitions, as well as in several Kaggle competitions. However, understanding why and how these methods work well for forecasting is still at a very early stage, partly due to their complexity. In this paper, I present a framework for regression-based ML that provides researchers with a common language and abstraction to aid in their study. To demonstrate the utility of the framework, I show how it can be used to map and compare ML methods used in the M5 Uncertainty competition. I then describe how the framework can be used together with ablation testing to systematically study their performance. Lastly, I use the framework to provide an overview of the solution space in regression-based ML forecasting, identifying areas for further research.     

Ranking professional forecasters by the predictive power of their narratives

This article presents the first ever ranking of professional forecasters based on the predictive power of the narrative of their regular research reports. The ranking is generated by applying the fully automated four-step procedure – called NLP-ForRank – developed in this article. The four steps are data scraping from the internet; data preparation; application of the natural language processing (NLP) models; and evaluation of the predictive power of the NLP indexes with linear regression, Granger causality, vector autoregression (VAR), and random forest forecasting models. Applying this procedure to five large Polish banks and to many time series shows that including the constructed NLP indexes in the forecasting models lowers the forecast errors, and that the optimal model almost always contains the NLP index. The financial news agencies could consider publishing this type of ranking on a regular basis as it would foster accountability, transparency, and a more competitive environment in the professional forecasting industry.     

Exchange-rate forecasts with simultaneous nearest-neighbour methods: evidence from the EMS

In this paper we extend nearest-neighbour predictors to allow for information content in a wider set of simultaneous time series. We apply these simultaneous nearest-neighbour (SNN) predictors to nine EMS currencies, using daily data for the 1st January 1978–31st December 1994 period. When forecasting performance is measured by Theil's U statistic, the (nonlinear) SNN predictors perform marginally better than both a random walk and the traditional (linear) ARIMA predictors. Furthermore, the SNN predictors outperform the random walk and the ARIMA models when producing directional forecasts.When formally testing for forecast accuracy, in most of the cases the SNN predictor outperforms the random walk at the 1% significance level, while outperforming the ARIMA model in three of the nine cases. On the other hand, our results suggest that the probability of correctly predicting the sign of change is higher for the SNN predictions than the ARIMA case.     

A Flexible Tool for Model Building: the Relevant Transformation of the Inputs Network Approach (RETINA)*

A new method, called Relevant Transformation of the Inputs Network Approach is proposed as a tool for model building. It is designed around flexibility (with nonlinear transformations of the predictors of interest), selective search within the range of possible models, out‐of‐sample forecasting ability and computational simplicity. In tests on simulated data, it shows both a high rate of successful retrieval of the data generating process, which increases with the sample size and a good performance relative to other alternative procedures. A telephone service demand model is built to show how the procedure applies on real data.     

Semiparametric quantile averaging in the presence of high-dimensional predictors

The paper proposes a method for forecasting conditional quantiles. In practice, one often does not know the “true” structure of the underlying conditional quantile function, and in addition, we may have a large number of predictors. Focusing on such cases, we introduce a flexible and practical framework based on penalized high-dimensional quantile averaging. In addition to prediction, we show that the proposed method can also serve as a predictor selector. We conduct extensive simulation experiments to asses its prediction and variable selection performances for nonlinear and linear time series model designs. In terms of predictor selection, the approach tends to select the true set of predictors with minimal false positives. With respect to prediction accuracy, the method competes well even with the benchmark/oracle methods that know one or more aspects of the underlying quantile regression model. We further illustrate the merit of the proposed method by providing an application to the out-of-sample forecasting of U.S. core inflation using a large set of monthly macroeconomic variables based on FRED-MD database. The application offers several empirical findings.     

Machine learning algorithms for forecasting and backcasting blood demand data with missing values and outliers: A study of Tema General Hospital of Ghana

The major challenge in managing blood products lies in the uncertainty of blood demand and supply, with a trade-off between shortage and wastage, especially in most developing countries. Thus, reliable demand predictions can be imperative in planning voluntary blood donation campaigns and improving blood availability within Ghana hospitals. However, most historical datasets on blood demand in Ghana are predominantly contaminated with missing values and outliers due to improper database management systems. Consequently, time-series prediction can be challenging since data cleaning can affect models’ predictive power. Also, machine learning (ML) models’ predictive power for backcasting past years’ lost data is understudied compared to their forecasting abilities. This study thus aims to compare K-Nearest Neighbour regression (KNN), Generalised Regression Neural Network (GRNN), Neural Network Auto-regressive (NNAR), Multi-Layer Perceptron (MLP), Extreme Learning Machine (ELM) and Long Short-Term Memory (LSTM) models via a rolling-origin strategy, for forecasting and backcasting a blood demand data with missing values and outliers from a government hospital in Ghana. KNN performed well in forecasting blood demand (12.55% error); whereas, ELM achieved the highest backcasting power (19.36% error). Future studies can also employ ML algorithms as a good alternative for backcasting past values of time-series data that are time-reversible.     

The value added by machine learning approaches in forecasting

This discussion reflects on the results of the M4 forecasting competition, and in particular, the impact of machine learning (ML) methods. Unlike the M3, which included only one ML method (an automatic artificial neural network that performed poorly), M4’s 49 participants included eight that used either pure ML approaches, or ML in conjunction with statistical methods. The six pure (or combination of pure) ML methods again fared poorly, with all of them falling below the Comb benchmark that combined three simple time series methods. However, utilizing ML either in combination with statistical methods (and for selecting weightings) or in a hybrid model with exponential smoothing not only exceeded the benchmark, but performed at the top. While these promising results by no means prove ML to be a panacea, they do challenge the notion that complex methods do not add value to the forecasting process.     

Machine learning advances for time series forecasting

In this paper, we survey the most recent advances in supervised machine learning (ML) and high-dimensional models for time-series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods, we pay special attention to penalized regressions and ensemble of models. The nonlinear methods considered in the paper include shallow and deep neural networks, in their feedforward and recurrent versions, and tree-based methods, such as random forests and boosted trees. We also consider ensemble and hybrid models by combining ingredients from different alternatives. Tests for superior predictive ability are briefly reviewed. Finally, we discuss application of ML in economics and finance and provide an illustration with high-frequency financial data.     

Effective judgmental forecasting in the context of fashion products

We study the conditions that influence judgmental forecasting effectiveness when predicting demand in the context of fashion products. Human judgment is of practical importance in this setting. Our goal is to investigate what type of decision support, in particular historical and/or contextual predictors, should be provided to human forecasters to improve their ability to detect and exploit linear and nonlinear cue–criterion relationships in the task environment. Using a field experiment on new product forecasts in the music industry, our analysis reveals that when forecasters are concerned with predictive accuracy and only managerial judgments are employed, providing both types of decision support data is beneficial. However, if judgmental forecasts are combined with a statistical forecast, restricting the decision support provided to human judges to contextual anchors is beneficial. We identify two novel interactions demonstrating that the exploitation of nonlinearities is easiest for human judgment if contextual data are present but historical data are absent. Thus, if the role of human judgment is to detect these nonlinearities (and the linearities are taken care of by some statistical model with which judgments are combined), then a restriction of the decision support provided makes sense. Implications for the theory and practice of building decision support models are discussed.     

Forecasting high resolution electricity demand data with additive models including smooth and jagged components

Short-Term Load Forecasting (STLF) is a fundamental instrument in the efficient operational management and planning of electric utilities. Emerging smart grid technologies pose new challenges and opportunities. Although load forecasting at the aggregate level has been extensively studied, electrical load forecasting at fine-grained geographical scales of households is more challenging. Among existing approaches, semi-parametric generalized additive models (GAM) have been increasingly popular due to their accuracy, flexibility, and interpretability. Their applicability is justified when forecasting is addressed at higher levels of aggregation, since the aggregated load pattern contains relatively smooth additive components. High resolution data are highly volatile, forecasting the average load using GAM models with smooth components does not provide meaningful information about the future demand. Instead, we need to incorporate irregular and volatile effects to enhance the forecast accuracy. We focus on the analysis of such hybrid additive models applied on smart meters data and show that it leads to improvement of the forecasting performances of classical additive models at low aggregation levels.     

Boosting diffusion indices

In forecasting and regression analysis, it is often necessary to select predictors from a large feasible set. When the predictors have no natural ordering, an exhaustive evaluation of all possible combinations of the predictors can be computationally costly. This paper considers ‘boosting’ as a methodology of selecting the predictors in factor‐augmented autoregressions. As some of the predictors are being estimated, we propose a stopping rule for boosting to prevent the model from being overfitted with estimated predictors. We also consider two ways of handling lags of variables: a componentwise approach and a block‐wise approach. The best forecasting method will necessarily depend on the data‐generating process. Simulations show that for each data type there is one form of boosting that performs quite well. When applied to four key economic variables, some form of boosting is found to outperform the standard factor‐augmented forecasts and is far superior to an autoregressive forecast. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting returns in the VIX futures market

This paper introduces a new forecasting model for VIX futures returns. The model is structural in nature and parsimonious, and contains parameters that are relatively easy to estimate. The forecasts of next day VIX futures returns based on this model are superior to those produced by a linear forecasting model that uses the same set of predictors. Moreover, the profits to a market-timing model based on the proposed forecasts are statistically and economically significant, and are robust to both the method used for adjusting for risk and transaction costs (up to around 15 basis points). In contrast, the forecasts generated by the linear forecasting model are not.