A comprehensive evaluation of macroeconomic forecasting methods

We employ datasets for seven developed economies and consider four classes of multivariate forecasting models in order to extend and enhance the empirical evidence in the macroeconomic forecasting literature. The evaluation considers forecasting horizons of between one quarter and two years ahead. We find that the structural model, a medium-sized DSGE model, provides accurate long-horizon US and UK inflation forecasts. We strike a balance between being comprehensive and producing clear messages by applying meta-analysis regressions to 2,976 relative accuracy comparisons that vary with the forecasting horizon, country, model class and specification, number of predictors, and evaluation period. For point and density forecasting of GDP growth and inflation, we find that models with large numbers of predictors do not outperform models with 13–14 hand-picked predictors. Factor-augmented models and equal-weighted combinations of single-predictor mixed-data sampling regressions are a better choice for dealing with large numbers of predictors than Bayesian VARs.     

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.     

Forecasting economic time series using targeted predictors

This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be non-linear. Second, the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series. This is accomplished by applying the method of principal components to ‘targeted predictors’ selected using hard and soft thresholding rules. Our three main findings can be summarized as follows. First, we find improvements at all forecast horizons over the current diffusion index forecasts by estimating the factors using fewer but informative predictors. Allowing for non-linearity often leads to additional gains. Second, forecasting the volatile one month ahead inflation warrants a high degree of targeting to screen out the noisy predictors. A handful of variables, notably relating to housing starts and interest rates, are found to have systematic predictive power for inflation at all horizons. Third, the targeted predictors selected by both soft and hard thresholding changes with the forecast horizon and the sample period. Holding the set of predictors fixed as is the current practice of factor forecasting is unnecessarily restrictive.     

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 national activity using lots of international predictors: An application to New Zealand

We assess the marginal predictive content of a large international dataset for forecasting GDP in New Zealand, an archetypal small open economy. We apply “data-rich” factor and shrinkage methods to efficiently handle hundreds of predictor series from many countries. The methods covered are principal components, targeted predictors, weighted principal components, partial least squares, elastic net and ridge regression. We find that exploiting a large international dataset can improve forecasts relative to data-rich approaches based on a large national dataset only, and also relative to more traditional approaches based on small datasets. This is in spite of New Zealand’s business and consumer confidence and expectations data capturing a substantial proportion of the predictive information in the international data. The largest forecasting accuracy gains from including international predictors are at longer forecast horizons. The forecasting performance achievable with the data-rich methods differs widely, with shrinkage methods and partial least squares performing best in handling the international data.     

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.     

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 bulk prices of Bordeaux wines using leading indicators

Agricultural price forecasting has been being abandoned progressively by researchers ever since the development of large-scale agricultural futures markets. However, as with many other agricultural goods, there is no futures market for wine. This paper draws on the agricultural prices forecasting literature to develop a forecasting model for bulk wine prices. The price data include annual and monthly series for various wine types that are produced in the Bordeaux region. The predictors include several leading economic indicators of supply and demand shifts. The stock levels and quantities produced are found to have the highest predictive power. The preferred annual and monthly forecasting models outperform naive random walk forecasts by 27.1% and 3.4% respectively; their mean absolute percentage errors are 2.7% and 3.4% respectively. A simple trading strategy based on monthly forecasts is estimated to increase profits by 3.3% relative to a blind strategy that consists of always selling at the spot price.     

Spotting the Danger Zone: Forecasting Financial Crises With Classification Tree Ensembles and Many Predictors

This paper introduces classification tree ensembles (CTEs) to the banking crisis forecasting literature. I show that CTEs substantially improve out‐of‐sample forecasting performance over best‐practice early‐warning systems. CTEs enable policymakers to correctly forecast 80% of crises with a 20% probability of incorrectly forecasting a crisis. These findings are based on a long‐run sample (1870–2011), and two broad post‐1970 samples which together cover almost all known systemic banking crises. I show that the marked improvement in forecasting performance results from the combination of many classification trees into an ensemble, and the use of many predictors. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal model averaging forecasting in high-dimensional survival analysis

This article considers ultrahigh-dimensional forecasting problems with survival response variables. We propose a two-step model averaging procedure for improving the forecasting accuracy of the true conditional mean of a survival response variable. The first step is to construct a class of candidate models, each with low-dimensional covariates. For this, a feature screening procedure is developed to separate the active and inactive predictors through a marginal Buckley–James index, and to group covariates with a similar index size together to form regression models with survival response variables. The proposed screening method can select active predictors under covariate-dependent censoring, and enjoys sure screening consistency under mild regularity conditions. The second step is to find the optimal model weights for averaging by adapting a delete-one cross-validation criterion, without the standard constraint that the weights sum to one. The theoretical results show that the delete-one cross-validation criterion achieves the lowest possible forecasting loss asymptotically. Numerical studies demonstrate the superior performance of the proposed variable screening and model averaging procedures over existing methods.     

Forecasting commodity prices out-of-sample: Can technical indicators help?

Economic variables are often used for forecasting commodity prices, but technical indicators have received much less attention in the literature. This paper demonstrates the predictability of commodity price changes using many technical indicators. Technical indicators are stronger predictors than economic indicators, and their forecasting performances are not affected by the problems of data mining or time changes. An investor with mean–variance preference receives utility gains of between 104.4 and 185.5 basis points from using technical indicators. Further analysis shows that technical indicators also perform better than economic variables for forecasting the density of commodity price changes.     

A control function approach for testing the usefulness of trending variables in forecast models and linear regression

Many predictors employed in forecasting macroeconomic and finance variables display a great deal of persistence. Tests for determining the usefulness of these predictors are typically oversized, overstating their importance. Similarly, hypothesis tests on cointegrating vectors will typically be oversized if there is not an exact unit root. This paper uses a control variable approach where adding stationary covariates with certain properties to the model can result in asymptotic normal inference for prediction regressions and cointegration vector estimates in the presence of possibly non-unit root trending covariates. The properties required for this result are derived and discussed.     

Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models

In a data-rich environment, forecasting economic variables amounts to extracting and organizing useful information from a large number of predictors. So far, the dynamic factor model and its variants have been the most successful models for such exercises. In this paper, we investigate a category of LASSO-based approaches and evaluate their predictive abilities for forecasting twenty important macroeconomic variables. These alternative models can handle hundreds of data series simultaneously, and extract useful information for forecasting. We also show, both analytically and empirically, that combing forecasts from LASSO-based models with those from dynamic factor models can reduce the mean square forecast error (MSFE) further. Our three main findings can be summarized as follows. First, for most of the variables under investigation, all of the LASSO-based models outperform dynamic factor models in the out-of-sample forecast evaluations. Second, by extracting information and formulating predictors at economically meaningful block levels, the new methods greatly enhance the interpretability of the models. Third, once forecasts from a LASSO-based approach are combined with those from a dynamic factor model by forecast combination techniques, the combined forecasts are significantly better than either dynamic factor model forecasts or the naïve random walk benchmark.     

Description, modelling and forecasting of data with optimal wavelets

Cascade processes have been used to model many different self-similar systems, as they are able to accurately describe most of their global statistical properties. The so-called optimal wavelet basis allows to achieve a geometrical representation of the cascade process-named microcanonical cascade- that describes the behavior of local quantities and thus it helps to reveal the underlying dynamics of the system. In this context, we study the benefits of using the optimal wavelet in contrast to other wavelets when used to define cascade variables, and we provide an optimality degree estimator that is appropriate to determine the closest-to-optimal wavelet in real data. Particularizing the analysis to stock market series, we show that they can be represented by microcanonical cascades in both the logarithm of the price and the volatility. Also, as a promising application in forecasting, we derive the distribution of the value of next point of the series conditioned to the knowledge of past points and the cascade structure, i.e., the stochastic kernel of the cascade process.     

Out‐of‐Sample Return Predictability: A Quantile Combination Approach

This paper develops a novel forecasting method that minimizes the effects of weak predictors and estimation errors on the accuracy of equity premium forecasts. The proposed method is based on an averaging scheme applied to quantiles conditional on predictors selected by LASSO. The resulting forecasts outperform the historical average, and other existing models, by statistically and economically meaningful margins. Copyright © 2016 John Wiley & Sons, Ltd.     

Sparse Partial Least Squares in Time Series for Macroeconomic Forecasting

Factor models have been applied extensively for forecasting when high‐dimensional datasets are available. In this case, the number of variables can be very large. For instance, usual dynamic factor models in central banks handle over 100 variables. However, there is a growing body of literature indicating that more variables do not necessarily lead to estimated factors with lower uncertainty or better forecasting results. This paper investigates the usefulness of partial least squares techniques that take into account the variable to be forecast when reducing the dimension of the problem from a large number of variables to a smaller number of factors. We propose different approaches of dynamic sparse partial least squares as a means of improving forecast efficiency by simultaneously taking into account the variable forecast while forming an informative subset of predictors, instead of using all the available ones to extract the factors. We use the well‐known Stock and Watson database to check the forecasting performance of our approach. The proposed dynamic sparse models show good performance in improving efficiency compared to widely used factor methods in macroeconomic forecasting. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting crude oil market volatility using variable selection and common factor

This paper aims to improve the predictability of aggregate oil market volatility with a substantially large macroeconomic database, including 127 macro variables. To this end, we use machine learning from both the variable selection (VS) and common factor (i.e., dimension reduction) perspectives. We first use the lasso, elastic net (ENet), and two conventional supervised learning approaches based on the significance level of predictors’ regression coefficients and the incremental R-square to select useful predictors relevant to forecasting oil market volatility. We then rely on the principal component analysis (PCA) to extract a common factor from the selected predictors. Finally, we augment the autoregression (AR) benchmark model by including the supervised PCA common index. Our empirical results show that the supervised PCA regression model can successfully predict oil market volatility both in-sample and out-of-sample. Also, the recommended models can yield forecasting gains in both statistical and economic perspectives. We further shed light on the nature of VS over time. In particular, option-implied volatility is always the most powerful predictor.     

基于小波变换和支持向量的国际原油价格预测

本文将小波分析与支持向量回归结合应用于国际原油价格预测,通过小波多尺度分析方法将油价时间序列分解为长期趋势和随机扰动项,然后采用支持向量回归对分解后的油价长期趋势进行预测。油价长期趋势的预测采用多因素预测方法,主要考虑市场供需基本面、库存、经济、投机等因素对石油价格走势的影响,建立多输入单输出的支持向量回归模型。实证研究表明,支持向量回归模型具有较高的预测性能,对原油价格长期趋势预测中,该方法比回归方法的预测精度高。     

Forecasting Bitcoin with technical analysis: A not-so-random forest?

This paper uses data sampled at hourly and daily frequencies to predict Bitcoin returns. We consider various advanced non-linear models based on a multitude of popular technical indicators that represent market trend, momentum, volume, and sentiment. We run a robust empirical exercise to observe the impact of forecast horizon, model type, time period, and the choice of inputs (predictors) on the forecast performance of the competing models. We find that Bitcoin prices are weakly efficient at the hourly frequency. In contrast, technical analysis combined with non-linear forecasting models becomes statistically significantly dominant relative to the random walk model on a daily horizon. Our comparative analysis identifies the random forest model as the most accurate at predicting Bitcoin. The estimated measures of the relative importance of predictors reveal that the nature of investing in the Bitcoin market evolved from trend-following to excessive momentum and sentiment in the most recent time period.