Measurement of Economic Forecast Accuracy: A Systematic Overview of the Empirical Literature
Abstract
:1. Introduction
2. Methodology
3. CitationBased Analysis
4. Content Analysis
4.1. Theoretical Background
4.2. Methodology Development
4.2.1. Measures
4.2.2. Statistical Tests
The MorganGrangerNewbold (MGN) Test
 $\left\{{y}_{t}:t=1,2,3,\dots ,\text{}T\right\}$ are actual values.
 $\left\{{\widehat{y}}_{t1}:t=1,2,3,\dots ,\text{}T\right\}$ and $\left\{{\widehat{y}}_{t2}:t=1,2,3,\dots ,\text{}T\right\}$ are two forecast values.
The DieboldMariano (DM) Test
 $\left\{{y}_{t}\right\}$ are actual data series.
 $\left\{{\widehat{y}}_{i,t}^{h}\right\}$ are the ith competing hstep forecasting series.
The HarveyLebourneNewbold (HLN) Tests
 (1)
 Variations of the MGN test
 (2)
 Modifications of the DieboldMariano (DM) test
4.2.3. Strategies
4.3. Empirical Findings
5. Conclusions
Funding
Informed Consent Statement
Conflicts of Interest
References
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Phase  Aim/s  Guideline Questions 

Phase 1: Designing the review  Research questions identified. Overall review approach considered. Research strategy established to identify relevant literature. 

Phase 2: Conducting the review  Articles selected, classified, and described. 

Phase 3: Analysis  Content analysis of selected research articles performed. 

Phase 4: Writing the review  Literature review reported and structured. 

Inclusion Criteria  Description 

Theoretical framework  Include all articles that offer a contribution to the development of a theoretical framework on the research topic. 
Methodology development  Include all studies that contribute to the development of methodology in the field of the analysis of economic forecasts accuracy. 
Empirical findings  Include all articles that contribute to the application to empirical research of the methods analyzed. 
Document Type  Number of Research Work  % of the Total 

Articles  340  84.4 
Proceeding Papers  51  12.7 
Review Articles  6  1.5 
Book Chapters  2  0.5 
Editorial Materials  2  0.5 
Early Access  1  0.2 
Reprints  1  0.2 
Total  403  100.0 
Serial Number  Title of the Journal  Number of Articles  Average Number of Citations Per Year from the Web of Science Core Collection 

1  International Journal of Forecasting  15  28.4 
2  Journal of Forecasting  13  10.04 
3  Economic Modelling  8  19.88 
4  Energies  8  10.63 
5  Journal of Business & Economic Statistics  8  148.62 
6  Romanian Journal of Economic Forecasting  6  1.1 
7  Applied Energy  5  46.25 
8  Empirical Economics  5  2.21 
9  Energy  5  12 
10  Journal of Econometrics  5  9 
11  Journal of Empirical Finance  4  2.6 
12  Quantitative Finance  4  3.4 
13  Technological Forecasting and Social Change  4  4.55 
14  Computational Economics  3  3 
15  European Journal of Operational Research  3  6 
16  Journal of Applied Econometrics  3  9.8 
17  Journal of Banking Finance  3  4.71 
18  Journal of Economic Behaviour Organization  3  9,7 
19  Journal of Economic Surveys  3  6.32 
20  Journal of Financial Economic Policy  3  1.1 
21  Renewable Energy  3  11.71 
22  Review of Accounting Studies  3  4.44 
23  Science of the Total Environment  3  21.67 
24  Sustainability  3  7 
25  Water  3  17.6 
No.  Title of the Paper  Author(s)  Number of Citations  Average Number of Citations Per Year  Year of Publication  Journal 

1  Comparing Predictive Accuracy  Diebold, F.X.; Mariano, R.S.  3340  128.46  1995  Journal of Business & Economic Statistics 
2  Error Measures for Generalizing About Forecasting MethodsEmpirical Comparisons  Armstrong, J.S.; Collopy, F.  637  21.97  1992  International Journal of Forecasting 
3  Economic and statistical measures of forecast accuracy  Granger, C.W.J.; Pesaran, M.H.  183  7.96  2000  Journal of Forecasting 
4  Review of guidelines for the use of combined forecasts  de Menezes, L.M.; Bunn, D.W.; Taylor, J.W.  122  5.81  2000  European Journal of Operational Research 
5  A ModelSelection Approach to Assessing The Information in the Term Structure Using LinearModels and Artificial Neural Networks  Swanson, N.R.; White, H.  122  4.69  1995  Journal of Business & Economic Statistics 
6  Can Internet Search Queries Help to Predict Stock Market Volatility?  Dimpfl, T.; Jank, S.  113  22.60  2016  European Financial Management 
7  Macroeconomic forecasts and microeconomic forecasters  Lamont, O.A.  99  5.21  2002  Journal of Economic Behaviour & Organization 
8  The state of macroeconomic forecasting  Fildes, R.; Stekler, H.  81  4.26  2002  Journal of Macroeconomics 
9  Cointegration and longhorizon forecasting  Christoffersen, P.F.; Diebold, F.X.  73  3.17  1998  Journal of Business & Economic Statistics 
10  How does Google search affect trader positions and crude oil prices?  Li, X.; Ma, J.; Wang, S.; Zhang, X.  64  10.67  2015  Economic Modelling 
11  The M3 competition: Statistical tests of the results  Koning, A.J.; Franses, P.H.; Hibon, M.; Stekler, H.O.  54  3.38  2005  International Journal of Forecasting 
12  Backtesting Parametric ValueatRisk With Estimation Risk  Escanciano, J.C.; Olmo, J.  54  4.91  2010  Journal of Business & Economic Statistics 
13  Credit Spreads as Predictors of RealTime Economic Activity: A Bayesian ModelAveraging Approach  Faust, J.; Gilchrist, S.; Wright; J.H.; Zakrajsek, E.  48  6.00  2013  Review of Economics and Statistics 
14  Tests of Equal Predictive Ability With RealTime Data  Clark, T.E.; McCracken, M.W.  40  3.33  2009  Journal of Business & Economic Statistics 
15  Do investor expectations affect sellside analysts’ forecast bias and forecast accuracy?  Walther, B.R.; Willis, R.H.  39  4.88  2013  Review of Accounting Studies 
16  Timevarying combinations of predictive densities using nonlinear filtering  Billio, M.; Casarin, R.; Ravazzolo, F.; van Dijk, H.K.  39  4.88  2013  Journal of Econometrics 
17  Forecast UncertaintyEx Ante and Ex Post: US Inflation and Output Growth  Clements, M.R.  37  5.29  2014  Journal of Business & Economic Statistics 
18  Improving the predictability of the oilUS stock nexus: The role of macroeconomic variables  Salisu, A.A.; Swaray, R.; Oloko, T.F.  36  18.00  2019  Economic Modelling 
19  The Measurement and Behavior of Uncertainty: Evidence from the ECB Survey of Professional Forecasters  Abel, J.; Rich, R.; Song, J.; Tracy, J.  29  5.80  2016  Journal of Applied Econometrics 
20  Generalised density forecast combinations  Kapetanios, G.; Mitchell, J.; Price, S.; Fawcett, N.  21  3.50  2015  Journal of Econometrics 
Measure  Symbol  Calculation  Explanation of Variables 

ScaleDependent Measures  
Mean Square Error  MSE  Mean $\left({e}_{t}^{2}\right)$  e_{t} denotes the forecast error. It is defined by the equation e_{t} = Y_{t}–F_{t}, where Y_{t} denotes the observation at time t and F_{t} denotes the forecast of Y_{t}. 
Root Mean Square Error  RMSE  $\sqrt{MSE}$  
Mean Absolute Error  MAE  $\mathrm{Mean}\text{}\left(\left{e}_{t}\right\right)$  
Median Absolute Error  MdAE  $\mathrm{Median}\text{}\left(\left{e}_{t}\right\right)$  
Measures Based on Percentage Error  
Mean Absolute Percentage Error  MAPE  $\mathrm{Mean}\text{}\left(\left{p}_{t}\right\right)$  The percentage error is the ratio between the forecast error and observation value: ${p}_{t}=\frac{{e}_{t}}{{Y}_{t}}100$. The advantage of percentage errors is scale independency, and therefore, it is a very common measure in the analysis of forecast performance across different datasets. 
Median Absolute Percentage Error  MdAPE  $\mathrm{Median}\text{}\left(\left{p}_{t}\right\right)$  
Root Mean Square Percentage Error  RMSPE  $\sqrt{mean\left({p}_{t}^{2}\right)}$  
Root Median Square Percentage Error  RMdSPE  $\sqrt{median\left({p}_{t}^{2}\right)}$  
Measures Based on Relative Errors  
Mean Relative Absolute Error  MRAE  $\mathrm{Mean}\text{}\left(\left{r}_{t}\right\right)$  r_{t} = e_{t} / e_{t}* is the relative error, where e_{t}* denotes the forecast error obtained from the benchmark method. Usually, the benchmark method is the random walk, where F_{t} is equal to the last observation. 
Median Relative Absolute Error  MdRAE  $\mathrm{Median}\text{}\left(\left{r}_{t}\right\right)$  
Geometric Mean Relative Absolute Error  GMRAE  $\mathrm{Gmean}\text{}\left(\left{r}_{t}\right\right)$  
Relative Measures  
Relative Mean Absolute Error  ReIMAE  $ReIMAE=\frac{MAE}{MA{E}_{b}}$  Instead of applying relative errors, the authors use relative measures. In the calculation of ReIMAE (Relative Mean Absolute Error), MAE_{b} denotes the MAE from the benchmark method. When the benchmark method is a random walk, and the forecasts are all onestep forecasts, the relative RMSE is Theil’s U statistic (Theil 1966), sometimes called U2. 
U Theil’s statistic (1)  U_{1}  ${U}_{1}=\frac{\sqrt{{{\displaystyle \sum}}_{t=1}^{n}{\left({a}_{t}{p}_{t}\right)}^{2}}}{\sqrt{{{\displaystyle \sum}}_{t=1}^{n}{a}_{t}^{2}}+\sqrt{{{\displaystyle \sum}}_{t=1}^{n}{p}_{t}^{2}}}$  
U Theil’s statistic (2)  U_{2}  ${U}_{2}=\sqrt{\frac{{{\displaystyle \sum}}_{t=1}^{n1}{\left(\frac{{p}_{t+1}{a}_{t+1}}{{a}_{t}}\right)}^{2}}{{{\displaystyle \sum}}_{t=1}^{n1}{\left(\frac{{a}_{t+1}{a}_{t}}{{a}_{t}}\right)}^{2}}}$ 
Measure  Symbol  Advantages  Limits 

ScaleDependent Measures  
Mean Square Error  MSE  Oftentimes, the RMSE is preferred to the MSE, as it is on the same scale as the data. Historically, the RMSE and MSE have been popular, largely because of their theoretical relevance in statistical modeling. The RMSE is useful as a relative measure to compare forecasts for the same series across different models. The smaller the error, the better the forecasting ability of that model according to the RMSE criterion. The mean absolute error (MAE) is less sensitive to large deviations than the usual squared loss.  Scaledependent measures are on the same scale as the data. Therefore, none of them are meaningful for assessing a method’s accuracy across multiple series. The sensitivity of the RMSE to outliers is the most common limitation of using of this measure. 
Root Mean Square Error  RMSE  
Mean Absolute Error  MAE  
Median Absolute Error  MdAE  
Measures Based on Percentage Error  
Mean Absolute Percentage Error  MAPE  Measures based on percentage errors have the advantage because they are scaleindependent. Therefore, they are frequently used to compare forecast accuracy between different data series. Additionally, these measures have an easy interpretation. In this group of measures, the Mean Absolute Percentage Error (MAPE) is the most applied measure.  These measures can produce infinite or undefined errors if zero values occur on the data. Moreover, percentage errors can have an extremely skewed distribution when the actual values are close to zero. 
Median Absolute Percentage Error  MdAPE  
Root Mean Square Percentage Error  RMSPE  
Root Median Square Percentage Error  RMdSPE  
Measures Based on Relative Errors  
Mean Relative Absolute Error  MRAE  Measures based on the relative errors are an alternative to the percentages for the calculation of scaleindependent measurements. They imply dividing each error by the error obtained using some benchmark method of forecasting. Since these measures are not scaledependent, they were recommended by Armstrong and Collopy (1992) and by Fildes (1992) for estimating the forecast accuracy across multiple series.  A deficiency of measures based on relative errors is that the forecast error obtained from the benchmark method can be small. In fact, the relative error has infinite variance because the forecast error obtained from the benchmark method has positive probability density at 0. When the errors are small, as they can be with intermittent series, use of the naïve method as a benchmark is no longer possible because it would involve division by zero. 
Median Relative Absolute Error  MdRAE  
Geometric Mean Relative Absolute Error  GMRAE  
Relative Measures  
Relative Mean Absolute Error  ReIMAE  An advantage of these methods is their interpretability. For example, relative MAE measures the improvement possible from the proposed forecast method relative to the benchmark forecast method. When RelMAE < 1, the proposed method is better than the benchmark method and when RelMAE > 1, the proposed method is worse than the benchmark method.  These measures require several forecasts on the same series to enable a MAE (or MSE) to be computed. One common situation where it is not possible to use such measures is where one is measuring the outofsample forecast accuracy at a single forecast horizon across multiple series. It makes no sense to compute the MAE across series (due to their different scales). 
U Theil’s statistic (1)  U_{1}  
U Theil’s statistic (2)  U_{2} 
Subject of Research  Title of the Paper  Author/s  Year of Publication  Empirical Findings 

Evaluation of economic forecast accuracy  The evaluation of economic forecasts  Mincer, Jacob, and Victor Zarnowitz  1969  Forecast accuracy decreases with an increase in length of the predictive span. 
Accuracy of Forecasting: An Empirical Investigation  Makridakis, Spyros, and Michele Hibon  1979  Simpler methods perform well compared to the more complex and statistically sophisticated ARMA models.  
Comparing exchange rate forecasting models: Accuracy versus profitability  Boothe, Paul, and Debra Glassman  1987  The highest economic forecast accuracy is realized applying simple timeseries models such as the random walk.  
The accuracy of economic forecasts related to GDP, unemployment, and inflation  Forecast smoothing and the optimal underutilization of information at the Federal Reserve  Scotese, Carol A.  1994  Testing forecasts for real GNP and inflation do not confirm significant biases in either the real GNP or inflation forecasts. 
An Evaluation of the Forecasts of the Federal Reserve: A Pooled Approach  Clements, Michael P., Fred Joutz, and Herman O. Stekler.  2007  There is evidence of systematic bias and of forecast smoothing of the inflation forecasts.  
Introduction to “The future of macroeconomic forecasting”  Heilemann, Ullrich, and Herman Stekler  2007  Unsuitable forecasting methods and unsuitable expectations regarding the degree of performance are the most important reasons for the lack of accuracy in G7 macroeconomic predictions.  
One Model and Various Experts: Evaluating Dutch Macroeconomic Forecasts  Franses, Philip Hans, Henk C. Kranendonk, and Debby Lanser  2011  The model forecasts are biased for a range of variables, and expert forecasts are far more accurate than the model forecasts, particularly when the forecast horizon is short.  
Strategies to Improve the Accuracy of Macroeconomic Forecasts in United States of America  Bratu, Mihaela  2012  The Holt–Winters method offers more accurate forecasts for inflation in the US when the initial expectations are provided by the Survey of Professional Forecasters.  
Comparing the accuracy of various econometric forecasting models  The Accuracy Assessment of Macroeconomic Forecasts based on Econometric Models for Romania  Simionescu, Mihaela  2014a  Comparing the accuracy of various econometric forecasting models (AR, VAR, and VARMA), it is concluded that vector autoregressive moving average (VARMA) models generate the most accurate forecasts. 
Testing of a tendency to overestimate economic growth  Lessons from OECD Forecasts during and after the Financial Crisis  Lewis, Christine, and Nigel Pain  2014  It is confirmed that economic growth is repeatedly overestimated in the projections, which failed to anticipate the extent of the slowdown and, later, the weak pace of the economic recovery. 
Evaluating the economic forecasts of FOMC members  Sheng, Xuguang  2015  The analysis of economic forecast accuracy concerning real GDP, inflation, and unemployment rates made by the Federal Open Market Committee confirmed a tendency to underpredict real GDP and overpredict inflation and unemployment rates.  
The accuracy of economic forecasts for the exchange rate  Comparing forecast performance of exchange rate models  Lam, Lillie, Laurence Fung, and Ipwing Yu  2008  Exchange rate predictability is explored using different theoretical and empirical models, such as the purchasing power parity, uncovered interest rate parity, and stickyprice monetary models, models based on the Bayesian model averaging technique, and a combination of these. The forecast based on combined models is more accurate than the forecast that uses only one model. 
Measuring forecast performance of ARMA & ARFIMA models: An application to US Dollar/UK pound foreign exchange rate  Shittu, Olanrewaju, I., and OlaOluwa S. Yaya  2009  Analyzing the forecast accuracy of ARIMA and ARFIMA models using the example of the US dollar/UK pound foreign exchange rate, it was concluded that estimated forecast values from the ARFIMA model is more realistic and closely reflects the current economic reality.  
The effects of business cycles on the accuracy of economic forecasts  How Accurate are Private Sector Forecasts? Crosscountry Evidence from Consensus Forecasts of Output Growth  Loungani, Prakash  2001  Forecasts for recessions are subject to a large systematic forecast error. 
Can the Fed Predict the State of the Economy?  Sinclair, Tara M., Herman O. Stekler, and Fred Joutz  2010  The Federal Reserve’s Greenbook projections overestimate the annual rate of change in real GDP in periods of recession and underestimate it in periods of economic growth.  
Systematic Errors in Growth Expectations over the Business Cycle  Dovern, Jonas, and Nils Jannsen  2017  Forecasts for recessions are subject to a large negative systematic forecast error, while forecasts for recoveries are subject to a positive systematic forecast error.  
How well do economists forecast recessions?  An, Zidong, Joao Tovar Jalles, and Parkash Loungani  2018  Forecasts are revised much more quickly in periods of recession than in nonrecession periods, but not rapidly enough to be able to avoid large forecast errors.  
Comparison in forecast accuracy among advanced and emerging economies  Information rigidities: Comparing average and individual forecasts for a large international panel  Dovern, Jonas, Urlich Fritsche, Prakash Loungani, and Natalia Tamirisa  2015  There are significant discrepancies in forecast performance among advanced and emerging economies, particularly in terms of forecast accuracy. 
How to improve the predictability of the oilUS stock nexus  Improving the predictability of the oil–US stock nexus: The role of macroeconomic variables  Salisu, Afees A., Raymond Swaray and Tirimisiyu F. Oloko  2019  ‘It is important to pretest the predictors for persistence, endogeneity, and conditional heteroscedasticity, particularly when modeling with highfrequency series’. 
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Buturac, G. Measurement of Economic Forecast Accuracy: A Systematic Overview of the Empirical Literature. J. Risk Financial Manag. 2022, 15, 1. https://doi.org/10.3390/jrfm15010001
Buturac G. Measurement of Economic Forecast Accuracy: A Systematic Overview of the Empirical Literature. Journal of Risk and Financial Management. 2022; 15(1):1. https://doi.org/10.3390/jrfm15010001
Chicago/Turabian StyleButurac, Goran. 2022. "Measurement of Economic Forecast Accuracy: A Systematic Overview of the Empirical Literature" Journal of Risk and Financial Management 15, no. 1: 1. https://doi.org/10.3390/jrfm15010001