Abstract
Artificial neural networks (ANNs) have been the catalyst to numerous advances in a variety of fields and disciplines in recent years. Their impact on economics, however, has been comparatively muted. One type of ANN, the long short-term memory network (LSTM), is particularly well-suited to deal with economic time-series. Here, the architecture’s performance and characteristics are evaluated in comparison with the dynamic factor model (DFM), currently a popular choice in the field of economic nowcasting. LSTMs are found to produce superior results to DFMs in the nowcasting of three separate variables; global merchandise export values and volumes, and global services exports. Further advantages include their ability to handle large numbers of input features in a variety of time frequencies. A disadvantage is the stochastic nature of outputs, common to all ANNs. In order to facilitate continued applied research of the methodology by avoiding the need for any knowledge of deep-learning libraries, an accompanying Python (Hopp 2021a) library was developed using PyTorch. The library is also available in R, MATLAB, and Julia.
References
1.
Amidi, A., and S. Amidi. 2019. “Recurrent Neural Networks Cheatsheet”. Recurrent Neural Networks Cheatsheet. 2019. Available at: https://stanford.edu/,shervine/teaching/cs-230/cheatsheet-recurrent-neural-networks. (accessed December 2020).
2.
Antolin-Diaz, J., T. Drechsel, and I. Petrella. 2020. Advances in Nowcasting Economic Activity: Secular Trends, Large Shocks and New Data . DOI: https://dx-doi-org.web.bisu.edu.cn/10.2139/ssrn.3669854.
3.
Banbura, M., D. Giannone, and L. Reichlin. 2010. Nowcasting . ECB Working Paper 1275. DOI: https://dx-doi-org.web.bisu.edu.cn/10.2139/ssrn.1717887.
4.
Bańbura, M, and G. Rünstler. 2011. “A Look into the Factor Model Black Box: Publication Lags and the Role of Hard and Soft Data in Forecasting GDP”. International Journal of Forecasting 27 (2): 333–346. DOI: https://doi.org/10.1016/j.ijforecast.2010.01.011.
5.
Bok, B., D. Caratelli, D. Giannone, A.M. Sbordone, and A. Tambalotti. 2018. “Macroeconomic Nowcasting and Forecasting with Big Data”. Annual Review of Economics 10 (1): 615–643. DOI: https://doi.org/10.1146/annurev-economics-080217-053214.
6.
Brownlee, J. 2018. Deep Learning for Time Series Forecasting: Predict the Future with MLPs, CNNs and LSTMs in Python . Machine Learning Mastery. Available at: https://books.google.ch/books?id=o5qnDwAAQBAJ.
7.
Buono, D., G. Mazzi, M. Marcellino, and Kapetanios. 2017. “Big Data Types for Macroeconomic Nowcasting”. Eurona .
8.
Camacho, M., Y. Lovcha, and G. Perez Quiros. 2015. “Can We Use Seasonally Adjusted Variables in Dynamic Factor Models?” Studies in Nonlinear Dynamics & Econometrics 19 (3): 377–391. DOI: https://doi.org/10.1515/snde-2013-0096.
9.
Cantú, F. 2018. Estimation of a Coincident Indicator for International Trade and Global Economic Activity . 27. UNCTAD Research Paper. UNCTAD. Available at: https://unctad.org/system/files/official-document/ser-rp-2018d9_en.pdf.
10.
Chernis, T., and R. Sekkel. 2017. “A Dynamic Factor Model for Nowcasting Canadian GDP Growth”. Empirical Economics 53(1): 217–234. DOI: https://doi.org/10.1007/s00181-017-1254-1.
11.
Chung, J.,Ç. Gülçehre, K. Cho, and Y. Bengio. 2014. “Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling”. CoRR abs/1412.3555. Available at: http://arxiv.org/abs/1412.3555.
12.
De Veaux, R.D., and L.H. Ungar. 1994. “Multicollinearity: A Tale of Two Nonparametric Regressions”. In Selecting Models from Data , edited by P. Cheeseman and R.W. Oldford, 393–402. New York, NY: Springer New York.
13.
Dematos, G., M.S. Boyd, B. Kermanshahi, N. Kohzadi, and I. Kaastra. 1996. “Feedforward versus Recurrent Neural Networks for Forecasting Monthly Japanese Yen Exchange Rates”. Financial Engineering and the Japanese Markets 3(1): 59–75. DOI: https://doi.org/10.1007/BF00868008.
14.
Domo. 2017. “Data Never Sleeps 5.0”. Data Never Sleeps 5.0 . 2017. Available: https://www.domo.com/learn/data-never-sleeps-5. (accessed September 2021).
15.
Doz, C., D. Giannone, and L. Reichlin. 2011. “A Two-Step Estimator for Large Approximate Dynamic Factor Models Based on Kalman Filtering”. Journal of Econometrics 164(1): 188–205. DOI: https://doi.org/10.1016/j.jeconom.2011.02.012.
16.
Einav, L., and J. Levin. 2014. “The Data Revolution and Economic Analysis”. Innovation Policy and the Economy 14: 1–24. DOI: https://doi.org/10.1086/674019.
17.
Engle, R.F. 1982. “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation”. Econometrica 50(4): 987–1007. DOI: https://doi.org/10.2307/1912773
18.
Ennett, C.M., M. Frize, and C.R. Walker. 2001. “Influence of Missing Values on Artificial Neural Network Performance.” Studies in Health Technology and Informatics 84 (1): 449–53.
19.
Falat, L., and L. Pancikova. 2015. “Quantitative Modelling in Economics with Advanced Artificial Neural Networks”. Procedia Economics and Finance 34: 194–201. DOI: https://doi.org/10.1016/S2212-5671(15)01619-6.
20.
Fan, F., J. Xiong, and G. Wang. 2020. “On Interpretability of Artificial Neural Networks”. CoRR abs/2001.02522. Available at: http://arxiv.org/abs/2001.02522.
21.
Federal Reserve Bank of New York. 2021. “Nowcasting Report: Methodology”. Nowcasting Report: Methodology . 2021. Available at: https://www.newyorkfed.org/research/policy/nowcast/methodology.html. (accessed November 2020)
22.
Giannone, D., L. Reichlin, and S. Simonelli. 2009. “Nowcasting Euro Area Economic Activity in Real Time: The Role of Confidence Indicators”. National Institute Economic Review 210 (1): 90–97. DOI: https://doi.org/10.1177/0027950109354413.
23.
Giannone, D., L. Reichlin, and D. Small. 2005. Nowcasting GDP and Inflation: The Real Time Informational Content of Macroeconomic Data Releases . Centre for Economic Policy Research. Available et: https://cepr.org/active/publications/discussion_papers/dp.php?dpno=5178.
24.
Giannone, D., L. Reichlin, and D. Small. 2008. “Nowcasting: The Real-Time Informational Content of Macroeconomic Data”. Journal of Monetary Economics 55(4): 665–666. DOI: https://doi.org/10.1016/j.jmoneco.2008.05.010.
25.
Grosse, R. 2017. Lecture 15: Exploding and Vanishing Gradients . Available at: http://www.cs.toronto.edu/,rgrosse/courses/csc321_2017/readings/L15%20Exploding%20and%20Vanishing%20Gradients.pdf. (accessed December 2020)
26.
Guichard, S., and E. Rusticelli. 2011. A Dynamic Factor Model for World Trade Growth: 874.OECD Economics Department Working Papers. DOI: https://doi.org/10.1787/5kg9zbvvwqq2-en.
27.
Gurney, K. 1997. An Introduction to Neural Networks. USA: Taylor & Francis, Inc..
28.
Hochreiter, S., and J. Schmidhuber. 1997. “Long Short-Term Memory”. Neural Computation 9: 1735–80. DOI: https://doi.org/10.1162/neco.1997.9.8.1735.
29.
Hodas, N.O., and P. Stinis. 2018. “Doing the Impossible: Why Neural Networks Can Be Trained at All”. Frontiers in Psychology 9: 1185. DOI: https://doi.org/10.3389/fpsyg.2018.01185.
30.
Hopp, D. 2021a. “nowcast_lstm”. Available at: https://github.com/dhopp1/nowcast_lstm/
31.
Hopp, D. 2021b. “nowcastLSTM”. Available at: https://github.com/dhopp1/nowcastLSTM/
32.
Hopp, D. 2021c. “nowcast_lstm_matlab”. Available at: https://github.com/dhopp1/nowcast_lstm_matlab/
33.
Hopp, D. 2021d. “NowcastLSTM.jl”. Available at: https://github.com/dhopp1/NowcastLSTM.jl/
34.
Johansen, S. 1995. Likelihood-Based Inference in Cointegrated Vector Autoregressive Models . New York.
35.
Keskar, N.S., D. Mudigere, J. Nocedal, M. Smelyanskiy, and P.T.P. Tang. 2017. On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima. Available at: https://arxiv.org/abs/1609.04836.
36.
Kozlov, M., S. Karaivanov, D. Tsonev, and R. Valkov. 2018. “The News on Norcasting”. The News on Nowcasting . Available at: https://www.weareworldquant.com/en/thought-leadership/the-news-on-nowcasting/. (accessed December 2020)
37.
Kurihara, Y., and A. Fukushima. 2019. “AR Model or Machine Learning for Forecasting GDP and Consumer Price for G7 Countries”. Applied Economics and Finance 6: 1. DOI: https://doi.org/10.11114/aef.v6i3.4126.
38.
Kuzin, V.N., M. Marcellino, and C. Schumacher. 2009. MIDAS versus Mixed-Frequency VAR: Nowcasting GDP in the Euro Area . Discussion Paper Series 1: Economic Studies 2009,07. Deutsche Bundesbank. Available at: https://ideas.repec.org/p/zbw/bubdp1/7576.html.
39.
Loermann, J., and B. Maas. 2019. Nowcasting US GDP with Artificial Neural Networks. MPRA Paper 95459. University Library of Munich, Germany. Available at: https://ideas.repec.org/p/pra/mprapa/95459.html.
40.
MacFeely, S. 2020. “In Search of the Data Revolution: Has the Official Statistics Paradigm Shifted?” Statistical Journal of the IAOS 36(4): 1075–1094. DOI: https://doi.org/10.3233/SJI-200662.
41.
Marcellino, M., and C. Schumacher. 2010. “Factor MIDAS for Nowcasting and Forecasting with Ragged-Edge Data: A Model Comparison for German GDP”. Oxford Bulletin of Economics and Statistics 72(4): 518–550.
42.
Mariano, R.S., and Y. Murasawa. 2003. “A New Coincident Index of Business Cycles Based on Monthly and Quarterly Series”. Journal of Applied Econometrics 18(4): 427–443. DOI: https://doi.org/10.1002/jae.695.
43.
Matheson, T. 2011. “New Indicators for Tracking Growth in Real Time”. IMF Working Paper 11 (43): 1–22.
44.
Molnar, C. 2019. Interpretable Machine Learning: A Guide for Making Black Box Models Explainable .
45.
Montavon, G., W. Samek, and K.-R. Müller. 2018. “Methods for Interpreting and Understanding Deep Neural Networks”. Digital Signal Processing 73: 1–15. DOI: https://doi.org/10.1016/j.dsp.2017.10.011.
46.
Morgado, A.J., L. Catela Nunes, and S. Salvado. 2007. Nowcasting an Economic Aggregate with Disaggregate Dynamic Factors: An Application to Portuguese GDP . GEE Papers 0002. Gabinete de Estratégia e Estudos, Ministério da Economia. Available at: https://ideas.repec.org/p/mde/wpaper/0002.html.
47.
Nielsen, M.A. 2015. “Neural Networks and Deep Learning.” Determination Press .
48.
Olah, C. 2015. Understanding LSTM Networks. Available at: https://colah.github.io/-posts/2015-08-Understanding-LSTMs/.
49.
OpenTable. 2021. “The State of the Restaurant Industry”. The State of the Restaurant Industry . Available at: https://www.opentable.com/state-of-industry. (accessed September 2021).
50.
Porshakov, A., A. Ponomarenko, and A. Sinyakov. 2016. “Nowcasting and Short-Term Forecasting of Russian GDP with a Dynamic Factor Model”. Journal of the New Economic Association 30(2): 60–76.
51.
PyTorch. 2021a. “Dropout”. Available at: https://pytorch.org/docs/stable/generated/-torch.nn.Dropout.html. (accessed October 2021)
52.
PyTorch. 2021b. “Loss Functions”. Available at: https://pytorch.org/docs/stable/nn.html#loss-functions. (accessed August 2021).
53.
PyTorch. 2021c. “LSTM”. Available at: https://pytorch.org/docs/stable/generated/-torch.nn.LSTM.html. (accessed October 2021).
54.
Rossiter, J. 2010. Nowcasting the Global Economy. 2010–2012 . Bank of Canada. Available at: https://ssrn.com/abstract=1674952. DOI: https://dx-doi-org.web.bisu.edu.cn/10.2139/ssrn.1674952.
55.
Rumelhart, D.E., G.E. Hinton, and R.J. Williams. 1986. “Learning Representations by Back-Propagating Errors”. Nature 323 (6088): 533–36. DOI: https://doi.org/10.1038/323533a0.
56.
Scikit-learn. 2021. “3.1. Cross-Validation: Evaluating Estimator Performance”. 3.1. Cross-Validation: Evaluating Estimator Performance . 2021. Availavle at: https://Scikit-learn.org/stable/modules/cross_validation.html. (accessed October 2021)
57.
Sharma, S., S. Sharma, and A. Athaiya. 2020. “Activation Functions in Neural Networks”. International Journal of Engineering Applied Sciences and Technology, 4(12): 310–316.
58.
Shi, X., Z. Chen, H. Wang, D.-Y. Yeung, W. Wong, and W. Woo. 2015. Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting .
59.
Smieja, M.Ł. Struski, J. Tabor, B. Zieliński, and P. Spurek. 2019. Processing of Missing Data by Neural Networks .
60.
Statista. 2021. “Coronavirus Impact on Retail E-Commerce Website Traffic Worldwide as of June 2020, by Average Monthly Visits”. Coronavirus Impact on Retail E-Commerce Website Traffic Worldwide as of June 2020, by Average Monthly Visits . 2021. Available at: https://www.statista.com/statistics/1112595/covid-19-impact-retail-e-commerce-site-traffic-global/. (accessed March 2021).
61.
Stock, J.H., and M.W. Watson. 2002. “Forecasting Using Principal Components From a Large Number of Predictors”. Journal of the American Statistical Association 97(460): 1167–1179. DOI: https://doi.org/10.11981016214502388618960.
62.
Stock, J.H., and M.W. Watson. 2004. “Combination Forecasts of Output Growth in a Seven-Country Data Set”. Journal of Forecasting 23(6): 405–430. DOI: https://doi.org/10.1002/for.928.
63.
Stratos, K. 2020. Feedforward and Recurrent Neural Networks . Available at: http://www1.cs.columbia.edu/,stratos/research/neural.pdf. (accessed December 2020)
64.
“Transforming Our World: The 2030 Agenda for Sustainable Development”. Transforming Our World: The 2030 Agenda for Sustainable Development . Available at:https://sdgs.un.org/2030agenda.
65.
UN. 2015. “Transforming Our World: The 2030 Agenda for Sustainable Development”. Transforming Our World: The 2030 Agenda for Sustainable Development . Available at: https://sdgs.un.org/2030agenda. (accessed September 2020).
66.
UNCTAD. 2020a. “UNCTADStat”. UNCTADStat . 2020. Available at: https://unctadstat.unctad.org/EN/Index.html. (accessed March 2021).
67.
UNCTAD. 2020b. “Global Merchandise Trade Nowcast December 2020”. Global Merchandise Trade Nowcast December 2020 . Available at: https://unctad.org/system/files/official-document/gdsdsimisc2020d8_en.pdf. (accessed August 2020).
68.
UNSD. 2020. “Nowcasting and Forecasting for SDG Monitoring”. Presented at the Nowcasting and Forecasting for SDG Monitoring, February 3, Geneva, Switzerland. Available at: https://unstats.un.org/unsd/statcom/51st-session/side-events/20200302-2L-Nowcasting-and-Forecasting-for-SDG-Monitoring/. (accessed February 2021).
69.
“The X-13ARIMA-SEATS Seasonal Adjustment Program”. The X-13ARIMA-SEATS Seasonal Adjustment Program . 2017. Available at:https://www.census.gov/srd/www/-x13as/.
70.
USCB. 2017. “The X-13ARIMA-SEATS Seasonal Adjustment Program”. The X-13ARIMA-SEATS Seasonal Adjustment Program . 2017. Available at: https://www.census.gov/srd/www/x13as/. (accessed March 2021).
71.
WMO. 2017. “Guidelines for Nowcasting Techniques”. 1198. WMO. WMO. Available at: https://library.wmo.int/doc_num.php?explnum_id=3795. (accessed March 2021).
72.
WTO. 2020. “Statistics on Merchandise Trade”. Statistics on Merchandise Trade . 2020. Available at: https://www.wto.org/english/res_e/statis_e/merch_trade_stat_e.htm. (accessed November 2020).
73.
Yilmazkuday, Hakan. 2021. “Stay-at-Home Works to Fight against COVID-19: International Evidence from Google Mobility Data”. Journal of Human Behavior in the Social Environment 31 (1–4): 210–220. DOI: https://doi.org/10.1080/10911359.2020.1845903.