Forecasting U.S. money growth using economic uncertainty measures and regularisation techniques

This paper examines the out-of-sample forecasting properties of six different economic uncertainty variables for the growth of the real M2 and real M4 Divisia money series for the U.S. using monthly data. The core contention is that information on economic uncertainty improves the forecasting accuracy. We estimate vector autoregressive models using the iterated rolling-window forecasting scheme, in combination with modern regularisation techniques from the field of machine learning. Applying the Hansen-Lunde-Nason model confidence set approach under two different loss functions reveals strong evidence that uncertainty variables that are related to financial markets, the state of the macroeconomy or economic policy provide additional informational content when forecasting monetary dynamics. The use of regularisation techniques improves the forecast accuracy substantially.     

Blending gradient boosted trees and neural networks for point and probabilistic forecasting of hierarchical time series

In this study, we addressed the problem of point and probabilistic forecasting by describing a blending methodology for machine learning models from the gradient boosted trees and neural networks families. These principles were successfully applied in the recent M5 Competition in both the Accuracy and Uncertainty tracks. The key points of our methodology are: (a) transforming the task into regression on sales for a single day; (b) information-rich feature engineering; (c) creating a diverse set of state-of-the-art machine learning models; and (d) carefully constructing validation sets for model tuning. We show that the diversity of the machine learning models and careful selection of validation examples are most important for the effectiveness of our approach. Forecasting data have an inherent hierarchical structure (12 levels) but none of our proposed solutions exploited the hierarchical scheme. Using the proposed methodology, we ranked within the gold medal range in the Accuracy track and within the prizes in the Uncertainty track. Inference code with pre-trained models are available on GitHub.¹     

Shrinkage Estimation Strategies in Generalised Ridge Regression Models: Low/High-Dimension Regime

In this study, we suggest pretest and shrinkage methods based on the generalised ridge regression estimation that is suitable for both multicollinear and high-dimensional problems. We review and develop theoretical results for some of the shrinkage estimators. The relative performance of the shrinkage estimators to some penalty methods is compared and assessed by both simulation and real-data analysis. We show that the suggested methods can be accounted as good competitors to regularisation techniques, by means of a mean squared error of estimation and prediction error. A thorough comparison of pretest and shrinkage estimators based on the maximum likelihood method to the penalty methods. In this paper, we extend the comparison outlined in his work using the least squares method for the generalised ridge regression.     

Real-time inflation forecasting using non-linear dimension reduction techniques

In this paper, we assess whether using non-linear dimension reduction techniques pays off for forecasting inflation in real-time. Several recent methods from the machine learning literature are adopted to map a large dimensional dataset into a lower-dimensional set of latent factors. We model the relationship between inflation and the latent factors using constant and time-varying parameter (TVP) regressions with shrinkage priors. Our models are then used to forecast monthly US inflation in real-time. The results suggest that sophisticated dimension reduction methods yield inflation forecasts that are highly competitive with linear approaches based on principal components. Among the techniques considered, the Autoencoder and squared principal components yield factors that have high predictive power for one-month- and one-quarter-ahead inflation. Zooming into model performance over time reveals that controlling for non-linear relations in the data is of particular importance during recessionary episodes of the business cycle or the current COVID-19 pandemic.     

Macroeconomic data transformations matter

In a low-dimensional linear regression setup, considering linear transformations/combinations of predictors does not alter predictions. However, when the forecasting technology either uses shrinkage or is nonlinear, it does. This is precisely the fabric of the machine learning (ML) macroeconomic forecasting environment. Pre-processing of the data translates to an alteration of the regularization – explicit or implicit – embedded in ML algorithms. We review old transformations and propose new ones, then empirically evaluate their merits in a substantial pseudo-out-sample exercise. It is found that traditional factors should almost always be included as predictors and moving average rotations of the data can provide important gains for various forecasting targets. Also, we note that while predicting directly the average growth rate is equivalent to averaging separate horizon forecasts when using OLS-based techniques, the latter can substantially improve on the former when regularization and/or nonparametric nonlinearities are involved.     

Forecasting ATM cash demands using a local learning model of cerebellar associative memory network

Forecasting cash demands at automatic teller machines (ATMs) is challenging, due to the heteroskedastic nature of such time series. Conventional global learning computational intelligence (CI) models, with their generalized learning behaviors, may not capture the complex dynamics and time-varying characteristics of such real-life time series data efficiently. In this paper, we propose to use a novel local learning model of the pseudo self-evolving cerebellar model articulation controller (PSECMAC) associative memory network to produce accurate forecasts of ATM cash demands. As a computational model of the human cerebellum, our model can incorporate local learning to effectively model the complex dynamics of heteroskedastic time series. We evaluated the forecasting performance of our PSECMAC model against the performances of current established CI and regression models using the NN5 competition dataset of 111 empirical daily ATM cash withdrawal series. The evaluation results show that the forecasting capability of our PSECMAC model exceeds that of the benchmark local and global-learning based models.     

Deep learning for modeling the collection rate for third-party buyers

This study evaluates a wide range of machine learning techniques such as deep learning, boosting, and support vector regression to predict the collection rate of more than 65,000 defaulted consumer credits from the telecommunications sector that were bought by a German third-party company. Weighted performance measures were defined based on the value of exposure at default for comparing collection rate models. The approach proposed in this paper is useful for a third-party company in managing the risk of a portfolio of defaulted credit that it purchases. The main finding is that one of the machine learning models we investigate, the deep learning model, performs significantly better out-of-sample than all other methods that can be used by an acquirer of defaulted credits based on weighted-performance measures. By using unweighted performance measures, deep learning and boosting perform similarly. Moreover, we find that using a training set with a larger proportion of the dataset does not improve prediction accuracy significantly when deep learning is used. The general conclusion is that deep learning is a potentially performance-enhancing tool for credit risk management.     

Modern Strategies for Time Series Regression

This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been proposed recently in the machine learning literature. The approaches are compared and contrasted, and it will be seen that there are advantages and disadvantages to most currently available approaches. There is ample room for methodological developments in this area. The work is motivated by an application involving the prediction of water levels as a function of rainfall and other climate variables in an aquifer in eastern Australia.     

Discussion

I thoroughly enjoyed reading the article by Bhadra et. al. (2020) and convey my congratulations to the authors for providing a comprehensive and coherent review of horseshoe-based regularization approaches for machine learning models. I am thankful to the editors for providing this opportunity to write a discussion on this useful article, which I expect will turn out to be a good guide in the future for statisticians and practitioners alike. It is quite amazing to see the rapid progress and the magnitude of work advancing the horseshoe regularization approach since the seminal paper by Carvalho et al. (2010). The current review article is a testimony for this. While I have been primarily working with continuous spike and slab priors for high-dimensional Bayesian modeling, I have been following the literature on horseshoe regularization with a keen interest. For my comments on this article, I will focus on some comparisons between these two approaches particularly in terms of model building and methodology and some computational considerations. I would like to first provide some comments on performing valid inference based on the horsheshoe prior framework.     

Modeling and predicting U.S. recessions using machine learning techniques

The most representative machine learning techniques are implemented for modeling and forecasting U.S. economic activity and recessions in particular. An elaborate, comprehensive, and comparative framework is employed in order to estimate U.S. recession probabilities. The empirical analysis explores the predictive content of numerous well-followed macroeconomic and financial indicators, but also introduces a set of less-studied predictors. The predictive ability of the underlying models is evaluated using a plethora of statistical evaluation metrics. The results strongly support the application of machine learning over more standard econometric techniques in the area of recession prediction. Specifically, the analysis indicates that penalized Logit regression models, k-nearest neighbors, and Bayesian generalized linear models largely outperform ‘original’ Logit/Probit models in the prediction of U.S. recessions, as they achieve higher predictive accuracy across long-, medium-, and short-term forecast horizons.     

A Survey of L1 Regression

L₁ regularization, or regularization with an L₁ penalty, is a popular idea in statistics and machine learning. This paper reviews the concept and application of L₁ regularization for regression. It is not our aim to present a comprehensive list of the utilities of the L₁ penalty in the regression setting. Rather, we focus on what we believe is the set of most representative uses of this regularization technique, which we describe in some detail. Thus, we deal with a number of L₁‐regularized methods for linear regression, generalized linear models, and time series analysis. Although this review targets practice rather than theory, we do give some theoretical details about L₁‐penalized linear regression, usually referred to as the least absolute shrinkage and selection operator (lasso).     

Application of Shrinkage Techniques in Logistic Regression Analysis: A Case Study

Logistic regression analysis may well be used to develop a predictive model for a dichotomous medical outcome, such as short-term mortality. When the data set is small compared to the number of covariables studied, shrinkage techniques may improve predictions. We compared the performance of three variants of shrinkage techniques: 1) a linear shrinkage factor, which shrinks all coefficients with the same factor; 2) penalized maximum likelihood (or ridge regression), where a penalty factor is added to the likelihood function such that coefficients are shrunk individually according to the variance of each covariable; 3) the Lasso, which shrinks some coefficients to zero by setting a constraint on the sum of the absolute values of the coefficients of standardized covariables.
Logistic regression models were constructed to predict 30-day mortality after acute myocardial infarction. Small data sets were created from a large randomized controlled trial, half of which provided independent validation data. We found that all three shrinkage techniques improved the calibration of predictions compared to the standard maximum likelihood estimates. This study illustrates that shrinkage is a valuable tool to overcome some of the problems of overfitting in medical data.     

Nowcasting and forecasting GDP in emerging markets using global financial and macroeconomic diffusion indexes

This paper contributes to the nascent literature on nowcasting and forecasting GDP in emerging market economies using big data methods. This is done by analyzing the usefulness of various dimension-reduction, machine learning and shrinkage methods, including sparse principal component analysis (SPCA), the elastic net, the least absolute shrinkage operator, and least angle regression when constructing predictions using latent global macroeconomic and financial factors (diffusion indexes) in a dynamic factor model (DFM). We also utilize a judgmental dimension-reduction method called the Bloomberg Relevance Index (BRI), which is an index that assigns a measure of importance to each variable in a dataset depending on the variable’s usage by market participants. Our empirical analysis shows that, when specified using dimension-reduction methods (particularly BRI and SPCA), DFMs yield superior predictions relative to both benchmark linear econometric models and simple DFMs. Moreover, global financial and macroeconomic (business cycle) diffusion indexes constructed using targeted predictors are found to be important in four of the five emerging market economies that we study (Brazil, Mexico, South Africa, and Turkey). These findings point to the importance of spillover effects across emerging market economies, and underscore the significance of characterizing such linkages parsimoniously when utilizing high-dimensional global datasets.     

Methods and Tools for Bayesian Variable Selection and Model Averaging in Normal Linear Regression

In this paper, we briefly review the main methodological aspects concerned with the application of the Bayesian approach to model choice and model averaging in the context of variable selection in regression models. This includes prior elicitation, summaries of the posterior distribution and computational strategies. We then examine and compare various publicly available R‐packages, summarizing and explaining the differences between packages and giving recommendations for applied users. We find that all packages reviewed (can) lead to very similar results, but there are potentially important differences in flexibility and efficiency of the packages.     

Preventing rather than punishing: An early warning model of malfeasance in public procurement

Is it possible to predict malfeasance in public procurement? With the proliferation of e-procurement systems in the public sector, anti-corruption agencies and watchdog organizations have access to valuable sources of information with which to identify transactions that are likely to become troublesome and why. In this article, we discuss the promises and challenges of using machine learning models to predict inefficiency and corruption in public procurement. We illustrate this approach with a dataset with more than two million public procurement contracts in Colombia. We trained machine learning models to predict which of them will result in corruption investigations, a breach of contract, or implementation inefficiencies. We then discuss how our models can help practitioners better understand the drivers of corruption and inefficiency in public procurement. Our approach will be useful to governments interested in exploiting large administrative datasets to improve the provision of public goods, and it highlights some of the tradeoffs and challenges that they might face throughout this process.     

Mixed-frequency machine learning: Nowcasting and backcasting weekly initial claims with daily internet search volume data

We propose an out-of-sample prediction approach that combines unrestricted mixed-data sampling with machine learning (mixed-frequency machine learning, MFML). We use the MFML approach to generate a sequence of nowcasts and backcasts of weekly unemployment insurance initial claims based on a rich trove of daily Google Trends search volume data for terms related to unemployment. The predictions are based on linear models estimated via the LASSO and elastic net, nonlinear models based on artificial neural networks, and ensembles of linear and nonlinear models. Nowcasts and backcasts of weekly initial claims based on models that incorporate the information in the daily Google Trends search volume data substantially outperform those based on models that ignore the information. Predictive accuracy increases as the nowcasts and backcasts include more recent daily Google Trends data. The relevance of daily Google Trends data for predicting weekly initial claims is strongly linked to the COVID-19 crisis.     

Forecasting football results and exploiting betting markets: The case of “both teams to score”

The continuous growth of available football data presents unprecedented research opportunities for a better understanding of football dynamics. While many research works focus on predicting which team will win a match, other interesting questions, such as whether both teams will score in a game, are still unexplored and have gained momentum with the rise of betting markets. With this in mind, we investigate the following research questions in this paper: “How difficult is the ‘both teams to score’ (BTTS) prediction problem?”, “Are machine learning classifiers capable of predicting BTTS better than bookmakers?”, and “Are machine learning classifiers useful for devising profitable betting strategies in the BTTS market?”. We collected historical football data, extracted groups of features to represent the teams’ strengths, and fed these to state-of-the-art classification models. We performed a comprehensive set of experiments and showed that, although hard to predict, in some scenarios it is possible to outperform bookmakers, which are robust baselines per se. More importantly, in some cases it is possible to beat the market and devise profitable strategies based on machine learning algorithms. The results are encouraging and, besides shedding light on the problem, may provide novel insights for all kinds of football stakeholders.     

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.     

Varying Coefficient Regression Models: A Review and New Developments

Varying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models and to discuss their extensions with some new developments. The new developments enable us to use different amount of smoothing for estimating different component functions in the models. They are for a flexible form of varying coefficient models that requires smoothing across different covariates' spaces and are based on the smooth backfitting technique that is admitted as a powerful technique for fitting structural regression models and is also known to free us from the curse of dimensionality.     

Optimal weighted average power similar tests for the covariance structure in the linear regression model

This paper suggests a procedure for the construction of optimal weighted average power similar tests for the error covariance matrix of a Gaussian linear regression model when the alternative model belongs to the exponential family. The paper uses a saddlepoint approximation to construct simple test statistics for a large class of problems and overcomes the computational burden of evaluating the complicated integrals arising in the derivation of optimal weighted average power tests. Extensions to panel data models are considered. Applications are given to tests for error autocorrelation in the linear regression model and in a panel data framework.