Forecasting crude oil futures market returns: A principal component analysis combination approach

To improve the predictability of crude oil futures market returns, this paper proposes a new combination approach based on principal component analysis (PCA). The PCA combination approach combines individual forecasts given by all PCA subset regression models that use all potential predictor subsets to construct PCA indexes. The proposed method can not only guard against over-fitting by employing the PCA technique but also reduce forecast variance due to extensive forecast combinations, thus benefiting from both the combination of information and the combination of forecasts. Showing impressive out-of-sample forecasting performance, the PCA combination approach outperforms a benchmark model and many related competing models. Furthermore, a mean–variance investor can realize sizeable utility gains by using the PCA combination forecasts relative to the competing forecasts from an asset allocation perspective.     

Predictive financial models of the euro area: A new evaluation test

This paper investigates the predictive ability of financial variables for euro area growth. Our forecasts are built from univariate autoregressive and single equation models. Euro area aggregate forecasts are constructed both by employing aggregate variables and by aggregating country-specific forecasts. The forecast evaluation is based on a recently developed test for equal predictive ability between nested models. Employing a monthly dataset from the period between January 1988 and May 2005 and setting the out-of-sample period to be from 2001 onwards, we find that the single most powerful predictor on a country basis is the stock market returns, followed by money supply growth. However, for the euro area aggregate, the set of most powerful predictors includes interest rate variables as well. The forecasts from pooling individual country models outperform those from the aggregate itself for short run forecasts, while for longer horizons this pattern is reversed. Additional benefits are obtained when combining information from a range of variables or combining model forecasts.     

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 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.     

Analysts' utilization of historical earnings information

This study examines whether security analysts (in)efficiently utilize the information contained in past series of annual and quarterly earnings in producing earnings forecasts. To do so, it investigates whether equal-weighted combinations of security analysts' forecasts with forecasts from statistical models based on historical earnings are superior, both in terms of being a better surrogate for the market's expectations of earnings and of accuracy, to forecasts from either one of these two sources. The empirical findings indicate that, although analysts' forecasts are superior to forecasts from statistical models, performance can be improved—both in terms of accuracy and also of being a better surrogate for market earnings expectations—by combining analysts' forecasts with forecasts from statistical models based on past quarterly earnings. Improvements in proxying for market earnings expectations were obtained even when analysts' forecasts made in June of the forecast year were used in the combinations. An implication of these findings is that investors can improve their investment decisions by using an average of the mean analysts' forecasts and the forecast produced by a time-series model of quarterly earnings in their investment decisions.     

Comparison of intraday probabilistic forecasting of solar irradiance using only endogenous data

Accurate solar forecasts are necessary to improve the integration of solar renewables into the energy grid. In recent years, numerous methods have been developed for predicting the solar irradiance or the output of solar renewables. By definition, a forecast is uncertain. Thus, the models developed predict the mean and the associated uncertainty. Comparisons are therefore necessary and useful for assessing the skill and accuracy of these new methods in the field of solar energy.The aim of this paper is to present a comparison of various models that provide probabilistic forecasts of the solar irradiance within a very strict framework. Indeed, we consider focusing on intraday forecasts, with lead times ranging from 1 to 6 h. The models selected use only endogenous inputs for generating the forecasts. In other words, the only inputs of the models are the past solar irradiance data. In this context, the most common way of generating the forecasts is to combine point forecasting methods with probabilistic approaches in order to provide prediction intervals for the solar irradiance forecasts. For this task, we selected from the literature three point forecasting models (recursive autoregressive and moving average (ARMA), coupled autoregressive and dynamical system (CARDS), and neural network (NN)), and seven methods for assessing the distribution of their error (linear model in quantile regression (LMQR), weighted quantile regression (WQR), quantile regression neural network (QRNN), recursive generalized autoregressive conditional heteroskedasticity (GARCHrls), sieve bootstrap (SB), quantile regression forest (QRF), and gradient boosting decision trees (GBDT)), leading to a comparison of 20 combinations of models.None of the model combinations clearly outperform the others; nevertheless, some trends emerge from the comparison. First, the use of the clear sky index ensures the accuracy of the forecasts. This derived parameter permits time series to be deseasonalized with missing data, and is also a good explanatory variable of the distribution of the forecasting errors. Second, regardless of the point forecasting method used, linear models in quantile regression, weighted quantile regression and gradient boosting decision trees are able to forecast the prediction intervals accurately.     

Forecasting football match results in national league competitions using score-driven time series models

We develop a new dynamic multivariate model for the analysis and forecasting of football match results in national league competitions. The proposed dynamic model is based on the score of the predictive observation mass function for a high-dimensional panel of weekly match results. Our main interest is in forecasting whether the match result is a win, a loss or a draw for each team. The dynamic model for delivering such forecasts can be based on three different dependent variables: the pairwise count of the number of goals, the difference between the numbers of goals, or the category of the match result (win, loss, draw). The different dependent variables require different distributional assumptions. Furthermore, different dynamic model specifications can be considered for generating the forecasts. We investigate empirically which dependent variable and which dynamic model specification yield the best forecasting results. We validate the precision of the resulting forecasts and the success of the forecasts in a betting simulation in an extensive forecasting study for match results from six large European football competitions. Finally, we conclude that the dynamic model for pairwise counts delivers the most precise forecasts while the dynamic model for the difference between counts is most successful for betting, but that both outperform benchmark and other competing models.     

Density Forecasts With Midas Models

We propose a parametric block wild bootstrap approach to compute density forecasts for various types of mixed‐data sampling (MIDAS) regressions. First, Monte Carlo simulations show that predictive densities for the various MIDAS models derived from the block wild bootstrap approach are more accurate in terms of coverage rates than predictive densities derived from either a residual‐based bootstrap approach or by drawing errors from a normal distribution. This result holds whether the data‐generating errors are normally independently distributed, serially correlated, heteroskedastic or a mixture of normal distributions. Second, we evaluate density forecasts for quarterly US real output growth in an empirical exercise, exploiting information from typical monthly and weekly series. We show that the block wild bootstrapping approach, applied to the various MIDAS regressions, produces predictive densities for US real output growth that are well calibrated. Moreover, relative accuracy, measured in terms of the logarithmic score, improves for the various MIDAS specifications as more information becomes available. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Forecast Pooling for European Macroeconomic Variables*

We compare alternative forecast pooling methods and 58 forecasts from linear, time‐varying and non‐linear models, using a very large dataset of about 500 macroeconomic variables for the countries in the European Monetary Union. On average, combination methods work well but single non‐linear models can outperform them for several series. The performance of pooled forecasts, and of non‐linear models, improves when focusing on a subset of unstable series, but the gains are minor. Finally, on average over the EMU countries, the pooled forecasts behave well for industrial production growth, unemployment and inflation, but they are often beaten by non‐linear models for each country and variable.     

Combining Forecasts from Nested Models*

Motivated by the common finding that linear autoregressive models often forecast better than models that incorporate additional information, this paper presents analytical, Monte Carlo and empirical evidence on the effectiveness of combining forecasts from nested models. In our analytics, the unrestricted model is true, but a subset of the coefficients is treated as being local‐to‐zero. This approach captures the practical reality that the predictive content of variables of interest is often low. We derive mean square error‐minimizing weights for combining the restricted and unrestricted forecasts. Monte Carlo and empirical analyses verify the practical effectiveness of our combination approach.     

REVERSE REGRESSIONS AND LONG‐HORIZON FORECASTING

Long‐horizon predictive regressions in finance pose formidable econometric problems when estimated using available sample sizes. Hodrick in 1992 proposed a remedy that is based on running a reverse regression of short‐horizon returns on the long‐run mean of the predictor. Unfortunately, this only allows the null of no predictability to be tested, and assumes stationary regressors. In this paper, we revisit long‐horizon forecasting from reverse regressions, and argue that reverse regression methods avoid serious size distortions in long‐horizon predictive regressions, even when there is some predictability and/or near unit roots. Meanwhile, the reverse regression methodology has the practical advantage of being easily applicable when there are many predictors. We apply these methods to forecasting excess bond returns using the term structure of forward rates, and find that there is indeed some return forecastability. However, confidence intervals for the coefficients of the predictive regressions are about twice as wide as those obtained with the conventional approach to inference. We also include an application to forecasting excess stock returns. Copyright © 2011 John Wiley & Sons, Ltd.     

A Simple Approach for Diagnosing Instabilities in Predictive Regressions

We introduce a method for detecting the presence of structural breaks in the parameters of predictive regressions linking noisy variables such as stock returns to persistent predictors such as valuation ratios. Our approach relies on the least squares‐based squared residuals of the predictive regression and is straightforward to implement. The distributions of the two test statistics we introduce are shown to be free of nuisance parameters, valid under dependent errors, already tabulated in the literature and robust to the degree of persistence of the chosen predictor. Our proposed method is subsequently applied to the predictability of US stock returns.     

Forecasting large datasets with Bayesian reduced rank multivariate models

The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance for US time series with the most promising existing alternatives, namely, factor models, large‐scale Bayesian VARs, and multivariate boosting. Specifically, we focus on classical reduced rank regression, a two‐step procedure that applies, in turn, shrinkage and reduced rank restrictions, and the reduced rank Bayesian VAR of Geweke ( 1996 ). We find that using shrinkage and rank reduction in combination rather than separately improves substantially the accuracy of forecasts, both when the whole set of variables is to be forecast and for key variables such as industrial production growth, inflation, and the federal funds rate. The robustness of this finding is confirmed by a Monte Carlo experiment based on bootstrapped data. We also provide a consistency result for the reduced rank regression valid when the dimension of the system tends to infinity, which opens the way to using large‐scale reduced rank models for empirical analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

A new approach to estimating earnings forecasting models: Robust regression MM-estimation

This study focuses on the impact of model estimation methods on earnings forecast accuracy. Compared with an ordinary least squares (OLS) regression combined with winsorization, robust regression MM-estimation improves the earnings forecast accuracy of all the models examined, especially for those with more variables. My findings indicate that the impact of outliers on the OLS regression increases with the number of variables in the models, alerting researchers who use OLS regressions for forecasting. My findings explain the puzzling negative relationship between earnings forecast accuracy and the number of model variables in prior research. Moreover, I demonstrate the valuation implications of earnings forecasted using robust regression MM-estimation. This study contributes to earnings forecasting, valuation, and influential observation treatment in forecasting.     

The effects of age structure on economic growth: An application of probabilistic forecasting to India

During recent years there has been an increasing awareness of the explanatory power of population age structure variables in economic growth regressions. We estimate a new cross-country regression model of the effects of age structure change on economic growth. We use the new model and recent probabilistic demographic forecasts for India to derive the uncertainty of predicted economic growth rates caused by the uncertainty in demographic developments.     

When product type experimental design is optimal? Brief survey and new results

In the paper the problem of optimum experimental design for estimating parameters of multivariate regression functions is considered. We address the question: under what conditions one can compose the optimal design from partial designs, obtained by considering partial regressions, which depend on reduced number of variables. After reinterpreting and reviewing briefly existing results we provide some new conditions.     

Tests of Predictive Ability for Vector Autoregressions Used for Conditional Forecasting

Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments. Even though conditional forecasting is common, there has been little work on methods for evaluating conditional forecasts. This paper provides analytical, Monte Carlo and empirical evidence on tests of predictive ability for conditional forecasts from estimated models. In the empirical analysis, we examine conditional forecasts obtained with a VAR in the variables included in the DSGE model of Smets and Wouters (American Economic Review 2007; 97 : 586–606). Throughout the analysis, we focus on tests of bias, efficiency and equal accuracy applied to conditional forecasts from VAR models. Copyright © 2016 John Wiley & Sons, Ltd.     

Probabilistic electricity price forecasting with NARX networks: Combine point or probabilistic forecasts?

Recent electricity price forecasting studies have shown that decomposing a series of spot prices into a long-term trend-seasonal and a stochastic component, modeling them independently and then combining their forecasts, can yield more accurate point predictions than an approach in which the same regression or neural network model is calibrated to the prices themselves. Here, considering two novel extensions of this concept to probabilistic forecasting, we find that (i) efficiently calibrated non-linear autoregressive with exogenous variables (NARX) networks can outperform their autoregressive counterparts, even without combining forecasts from many runs, and that (ii) in terms of accuracy it is better to construct probabilistic forecasts directly from point predictions. However, if speed is a critical issue, running quantile regression on combined point forecasts (i.e., committee machines) may be an option worth considering. Finally, we confirm an earlier observation that averaging probabilities outperforms averaging quantiles when combining predictive distributions in electricity price forecasting.     

Subjective evaluation of composite econometric policy inputs

Studies have suggested that a composite forecast may be preferred to a single forecast. In addition, forecasting objectives are often conflicting. For example, one forecast may have the smallest sum of absolute forecast errors, while another has the smallest maximum absolute error. This paper examines the appropriateness of using multiple objective linear programming to determine weighted linear combinations of forecasts to be used as inputs for policy analysis. An example is presented where the methodology is used to combine the forecasts for several policy variables. The forecasts are selected from large econometric, consensus, and univariate time series models.