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Industrial Output Growth Forecast: A Machine Learning Approach Based on Cross-Validation

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  2. Economics, Finance, Business & Management
  3. Applied Economics Quarterly
  4. Vol. 67, Issue 4
  5. pp. 337–351

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Marcondes Pinto, J., Marçal, E. Industrial Output Growth Forecast: A Machine Learning Approach Based on Cross-Validation. Applied Economics Quarterly, 67(4), 337-351. https://doi.org/10.3790/aeq.67.4.337
Marcondes Pinto, Jeronymo and Marçal, Emerson Fernandes "Industrial Output Growth Forecast: A Machine Learning Approach Based on Cross-Validation" Applied Economics Quarterly 67.4, 2021, 337-351. https://doi.org/10.3790/aeq.67.4.337
Marcondes Pinto, Jeronymo/Marçal, Emerson Fernandes (2021): Industrial Output Growth Forecast: A Machine Learning Approach Based on Cross-Validation, in: Applied Economics Quarterly, vol. 67, iss. 4, 337-351, [online] https://doi.org/10.3790/aeq.67.4.337
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Industrial Output Growth Forecast: A Machine Learning Approach Based on Cross-Validation

Marcondes Pinto, Jeronymo | Marçal, Emerson Fernandes

Applied Economics Quarterly, Vol. 67 (2021), Iss. 4 : pp. 337–351

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Article Details

Publisher Name
Duncker & Humblot
DOI
https://doi.org/10.3790/aeq.67.4.337
Language
English
Pages
15
Keywords

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Author Details

Jeronymo Marcondes Pinto, Corresponding author. Esplanada dos Ministérios, F Block, Floor 1, Ministry of Economics – SIT, Brasília/DF, Brazil.

Emerson Fernandes Marçal, Sao Paulo School of Economics and CEMAP-EESP-FGV, Rua Itapeva, 286, 10th floor, Sao Paulo – Brazil. Phone: +55-11-3799-3228.

References

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  23. Salinas, D./Flunkert, V./Gasthaus, J./Januschowski, T. (2019): “DeepAR: Probabilistic forecasting with autoregressive recurrent networks”, International Journal of Forecasting 36(3), 1181–1191.  Google Scholar
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  28. Tong, H. (1990): Non-linear time series: a dynamical system approach, Oxford University Press.  Google Scholar
  29. Zhang, Y./Yang, Y. (2015): “Cross-validation for selecting a model selection procedure”, Journal of Econometrics 187(1), 95–112.  Google Scholar
  30. Arlot, S./Celisse, A. et al. (2010): “A survey of cross-validation procedures for model selection”, Statistics Surveys 4, 40–79.  Google Scholar
  31. Bates, J. M./Granger, C. W. (1969): “The combination of forecasts”, Journal of the Operational Research Society 20(4), 451–468.  Google Scholar
  32. Bergmeir, C./Benítez, J. M. (2012): “On the use of cross-validation for time series predictor evaluation”, Information Sciences 191, 192–213.  Google Scholar
  33. Bergmeir, C./Costantini, M./Benítez, J. M. (2014): “On the usefulness of cross-validation for directional forecast evaluation”, Computational Statistics & Data Analysis 76, 132–143.  Google Scholar
  34. Bergmeir, C./Hyndman, R. J./Koo, B. et al. (2015): “A note on the validity of cross-validation for evaluating time series prediction”, Monash University Department of Econometrics and Business Statistics Working Paper 10, 15.  Google Scholar
  35. Chan, F./Pauwels, L. L. (2018): “Some theoretical results on forecast combinations”, International Journal of Forecasting 34(1), 64–74.  Google Scholar
  36. Cryer, J. D./Kellet, N. (1991): Time Series Analysis, Springer.  Google Scholar
  37. Fornaro, P./Luomaranta, H. (2020): “Nowcasting Finnish real economic activity: a machine learning approach”, Empirical Economics 58(1), 55–71.  Google Scholar
  38. Garcia, M. G./Medeiros, M. C./Vasconcelos, G. F. (2017): “Real-time inflation forecasting with high-dimensional models: The case of Brazil”, International Journal of Forecasting 33(3), 679–693.  Google Scholar
  39. Hamilton, J. D. (1994): Time Series Analysis, Princeton University Press.  Google Scholar
  40. Hansen, P. R./Lunde, A./Nason, J. M. (2011): “The model confidence set”, Econometrica 79(2), 453–497.  Google Scholar
  41. Harvey, D./Leybourne, S./Newbold, P. (1997): “Testing the equality of prediction mean squared errors”, International Journal of Forecasting 13(2), 281–291.  Google Scholar
  42. Hsiao, C./Wan, S. K. (2014): “Is there an optimal forecast combination?”, Journal of Econometrics 178, 294–309.  Google Scholar
  43. Hyndman, R./Khandakar, Y. (2008): “Automatic Time Series Forecasting: The Forecast Package for R”, Journal of Statistical Software, Articles 27(3), 1–22. doi:10.18637/jss.v027.i03, https://www.jstatsoft.org/v027/i03.  Google Scholar
  44. James, G./Witten, D./Hastie, T./Tibshirani, R. (2013): An Introduction to Statistical Learning, vol. 112, Springer.  Google Scholar
  45. Markatou, M./Tian, H./Biswas, S./Hripcsak, G. (2005): “Analysis of variance of cross-validation estimators of the generalization error”, Journal of Machine Learning Research 6(Jul), 1127–1168.  Google Scholar
  46. McKnight, S./Mihailov, A./Rumler, F. (2019): “Inflation forecasting using the New Keynesian Phillips Curve with a time-varying trend”, Economic Modelling.  Google Scholar
  47. Montero-Manso, P./Athanasopoulos, G./Hyndman, R. J./Talagala, T. S. (2020): “FFORMA: Feature-based forecast model averaging”, International Journal of Forecasting 36(1), 86–92.  Google Scholar
  48. Murphy, K. P. (2012): Machine learning: a probabilistic perspective, MIT press.  Google Scholar
  49. Panagiotelis, A./Athanasopoulos, G./Hyndman, R. J./Jiang, B./Vahid, F. (2019): “Macroeconomic forecasting for Australia using a large number of predictors”, International Journal of Forecasting 35(2), 616–633.  Google Scholar
  50. Pawlikowski, M./Chorowska, A. (2020): “Weighted ensemble of statistical models”, International Journal of Forecasting 36(1), 93–97.  Google Scholar
  51. Racine, J. (2000): “Consistent cross-validatory model-selection for dependent data: hv-block cross-validation”, Journal of Econometrics 99(1), 39–61.  Google Scholar
  52. Salinas, D./Flunkert, V./Gasthaus, J./Januschowski, T. (2019): “DeepAR: Probabilistic forecasting with autoregressive recurrent networks”, International Journal of Forecasting 36(3), 1181–1191.  Google Scholar
  53. Siliverstovs, B. (2020): “Assessing nowcast accuracy of US GDP growth in real time: the role of booms and busts”, Empirical Economics 58(1), 7–27.  Google Scholar
  54. Smeekes, S./Wijler, E. (2018): “Macroeconomic forecasting using penalized regression methods”, International Journal of Forecasting 34(3), 408–430.  Google Scholar
  55. Spiliotis, E./Assimakopoulos, V./Makridakis, S. (2020): “Generalizing the Theta method for automatic forecasting”, European Journal of Operational Research.  Google Scholar
  56. Timmermann, A. (2006): “Forecast combinations”, Handbook of Economic Forecasting 1, 135–196.  Google Scholar
  57. Tong, H. (1990): Non-linear time series: a dynamical system approach, Oxford University Press.  Google Scholar
  58. Zhang, Y./Yang, Y. (2015): “Cross-validation for selecting a model selection procedure”, Journal of Econometrics 187(1), 95–112.  Google Scholar
  59. Arlot, S./Celisse, A. et al. (2010): “A survey of cross-validation procedures for model selection”, Statistics Surveys 4, 40–79.  Google Scholar
  60. Bates, J. M./Granger, C. W. (1969): “The combination of forecasts”, Journal of the Operational Research Society 20(4), 451–468.  Google Scholar
  61. Bergmeir, C./Benítez, J. M. (2012): “On the use of cross-validation for time series predictor evaluation”, Information Sciences 191, 192–213.  Google Scholar
  62. Bergmeir, C./Costantini, M./Benítez, J. M. (2014): “On the usefulness of cross-validation for directional forecast evaluation”, Computational Statistics & Data Analysis 76, 132–143.  Google Scholar
  63. Bergmeir, C./Hyndman, R. J./Koo, B. et al. (2015): “A note on the validity of cross-validation for evaluating time series prediction”, Monash University Department of Econometrics and Business Statistics Working Paper 10, 15.  Google Scholar
  64. Chan, F./Pauwels, L. L. (2018): “Some theoretical results on forecast combinations”, International Journal of Forecasting 34(1), 64–74.  Google Scholar
  65. Cryer, J. D./Kellet, N. (1991): Time Series Analysis, Springer.  Google Scholar
  66. Fornaro, P./Luomaranta, H. (2020): “Nowcasting Finnish real economic activity: a machine learning approach”, Empirical Economics 58(1), 55–71.  Google Scholar
  67. Garcia, M. G./Medeiros, M. C./Vasconcelos, G. F. (2017): “Real-time inflation forecasting with high-dimensional models: The case of Brazil”, International Journal of Forecasting 33(3), 679–693.  Google Scholar
  68. Hamilton, J. D. (1994): Time Series Analysis, Princeton University Press.  Google Scholar
  69. Hansen, P. R./Lunde, A./Nason, J. M. (2011): “The model confidence set”, Econometrica 79(2), 453–497.  Google Scholar
  70. Harvey, D./Leybourne, S./Newbold, P. (1997): “Testing the equality of prediction mean squared errors”, International Journal of Forecasting 13(2), 281–291.  Google Scholar
  71. Hsiao, C./Wan, S. K. (2014): “Is there an optimal forecast combination?”, Journal of Econometrics 178, 294–309.  Google Scholar
  72. Hyndman, R./Khandakar, Y. (2008): “Automatic Time Series Forecasting: The Forecast Package for R”, Journal of Statistical Software, Articles 27(3), 1–22. doi:10.18637/jss.v027.i03, https://www.jstatsoft.org/v027/i03.  Google Scholar
  73. James, G./Witten, D./Hastie, T./Tibshirani, R. (2013): An Introduction to Statistical Learning, vol. 112, Springer.  Google Scholar
  74. Markatou, M./Tian, H./Biswas, S./Hripcsak, G. (2005): “Analysis of variance of cross-validation estimators of the generalization error”, Journal of Machine Learning Research 6(Jul), 1127–1168.  Google Scholar
  75. McKnight, S./Mihailov, A./Rumler, F. (2019): “Inflation forecasting using the New Keynesian Phillips Curve with a time-varying trend”, Economic Modelling.  Google Scholar
  76. Montero-Manso, P./Athanasopoulos, G./Hyndman, R. J./Talagala, T. S. (2020): “FFORMA: Feature-based forecast model averaging”, International Journal of Forecasting 36(1), 86–92.  Google Scholar
  77. Murphy, K. P. (2012): Machine learning: a probabilistic perspective, MIT press.  Google Scholar
  78. Panagiotelis, A./Athanasopoulos, G./Hyndman, R. J./Jiang, B./Vahid, F. (2019): “Macroeconomic forecasting for Australia using a large number of predictors”, International Journal of Forecasting 35(2), 616–633.  Google Scholar
  79. Pawlikowski, M./Chorowska, A. (2020): “Weighted ensemble of statistical models”, International Journal of Forecasting 36(1), 93–97.  Google Scholar
  80. Racine, J. (2000): “Consistent cross-validatory model-selection for dependent data: hv-block cross-validation”, Journal of Econometrics 99(1), 39–61.  Google Scholar
  81. Salinas, D./Flunkert, V./Gasthaus, J./Januschowski, T. (2019): “DeepAR: Probabilistic forecasting with autoregressive recurrent networks”, International Journal of Forecasting 36(3), 1181–1191.  Google Scholar
  82. Siliverstovs, B. (2020): “Assessing nowcast accuracy of US GDP growth in real time: the role of booms and busts”, Empirical Economics 58(1), 7–27.  Google Scholar
  83. Smeekes, S./Wijler, E. (2018): “Macroeconomic forecasting using penalized regression methods”, International Journal of Forecasting 34(3), 408–430.  Google Scholar
  84. Spiliotis, E./Assimakopoulos, V./Makridakis, S. (2020): “Generalizing the Theta method for automatic forecasting”, European Journal of Operational Research.  Google Scholar
  85. Timmermann, A. (2006): “Forecast combinations”, Handbook of Economic Forecasting 1, 135–196.  Google Scholar
  86. Tong, H. (1990): Non-linear time series: a dynamical system approach, Oxford University Press.  Google Scholar
  87. Zhang, Y./Yang, Y. (2015): “Cross-validation for selecting a model selection procedure”, Journal of Econometrics 187(1), 95–112.  Google Scholar

Abstract

Our work aims to evaluate two strategies to forecast industrial output growth, one of the important macroeconomic indicators for a country. Automatic algorithms that require few or no human interventions and are neutral generate good forecast performance and can be helpful for policymakers. We propose an automatic algorithm that is based on cross-validating different models and finding an optimal combination of them as soon as a new information is available. We evaluate two strategies. The first strategy aims to improve the Granger and Bates method by using cross-validation to better estimate the weights that are used in forecast combinations. The second strategy selects the best model to be used for forecasting based on the Cv technique (CvML). We apply our strategies to the industrial output growth rate data of six countries: Brazil, Germany, the United States, France, Japan, and the United Kingdom. Both cited methods were applied on “pseudo” streaming data, with observations feeding the model one by one, being re-estimated after each step, with an automatic selection/combination of models. Our results show that CvML outperforms all other benchmark models in most cases, especially in the long run. Even when CvML is not the best performing model, it has the same statistical performance as the best one.

Table of Contents

Section Title Page Action Price
Jeronymo Marcondes Pinto / Emerson Fernandes Marçal: Industrial Output Growth Forecast: A Machine Learning Approach Based on Cross-Validation 337
Abstract 337
1. Introduction 337
2. Material and Methods 339
2.1 Cross-Validation Parameters 340
2.2 Modified Granger and Bates Strategy 341
2.3 Cross-Validation Machine-Learning Strategy 342
2.4 Benchmarks 342
3. Results 343
3.1 Data 343
3.2 Findings 343
4. Limitations and Possible Extensions 345
5. Concluding Remarks 346
References 347
Appendix 349

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