Abstract
This paper compares several forecasting methods using high-dimensional macroeconomic data from Japan. The diffusion index (DI) model has been widely used to incorporate the information contained in high-dimensional data for forecasting. We propose two selection methods of the number of latent factors in the DI model and compare the DI model with the vector autoregression (VAR) model whose parameters are estimated by lasso-type methods. We find that the DI model tends to be better for short-horizon forecasting, whereas the VAR model tends to be better for long-horizon forecasting. Moreover, we find that the information exploited for forecasting is similar between the DI and VAR models.
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Notes
Our terminology may be slightly misleading, because we actually use observations in both the training and validation periods to obtain some forecasts. For instance, to obtain \({\hat{y}}_{i,T|T-h, \ldots , T-T_1}^\lambda\), we use the observation \(y_{T-h}\), which belongs to the validation period if \(h < T- T_1\). In this paper, the term “validation period” means that the MSFE is calculated over the period to determine the regularization parameter.
Due to recent doubt in employment related data credibility in Japan, a few series may be updated. However, the qualitative results of this paper will remain unaffected.
The dataset after transformation and implementation codes are available upon request.
Just for reference, we also compared our rolling window method with the 10-fold cross-validation that splits the sample randomly without taking account the time dependence of the observations. The result did not show a clear difference between the performance of two methods. We do not employ a simple K-fold cross-validation for our prediction problem, because it causes data leakage, that is, it uses the information of future observations to train a prediction model.
Because all variables are normalized to have variance unity, a high MSFE of the AR model implies that the variable is hard to predict.
References
Ahn, S. C., & Horenstein, A. R. (2013). Eigenvalue ratio test for the number of factors. Econometrica, 81(3), 1203–1227.
Altissimo, F., Cristadoro, R., Forni, M., Lippi, M., & Veronese, G. (2010). New Eurocoin: Tracking economic growth in real time. Review of Economics and Statistics, 92(4), 1024–1034.
Arlot, S., & Celisse, A. (2010). A survey of cross-validation procedures for model selection. Statistics Surveys, 4, 40–79.
Artis, M. J., Banerjee, A., & Marcellino, M. (2005). Factor forecasts for the UK. Journal of Forecasting, 24(4), 279–298.
Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica, 71(1), 135–171.
Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191–221.
Bai, J., & Ng, S. (2008). Forecasting economic time series using targeted predictors. Journal of Econometrics, 146(2), 304–317.
Banerjee, A., Marcellino, M., & Masten, I. (2008). Forecasting macroeconomic variables using diffusion indexes in short sample with structural change. In: Rapach DE, Wohar ME (eds) Forecasting in the Presence of Structural Breaks and Model Uncertainty, Emerald Group Publishing, chap 4, pp 149–194.
Bernanke, B. S., Boivin, J., & Ellasz, P. (2005). Measuring the effects of monetary policy: A factor-augumented vector autoregressive (FAVAR) approach. Quarterly Journal of Economics, 120(1), 387–422.
Boivin, J., & Giannoni, M. (2006). DSGE models in a data-rich environment, NBER Working Paper Series, No. 12772.
Burns, A. F., & Mitchell, W. C. (1946). Measuring Business Cycles. New York: NBER.
Callot, LAF., & Kock, AB. (2014). Oracle efficient estimation and forecasting with the adaptive lasso and the adaptive group lasso in vector autoregressions. In: Essays in Nonlinear Time Series Econometrics, Oxford University Press.
Chamberlain, G., & Rothschild, M. (1983). Arbitrage, factor structure, and mean-variance analysis on large asset markets. Econometrica, 51(5), 1281–1304.
Chikamatsu, K., Hirakata, N., Kido, Y., & Otaka, K. (2018). Nowcasting japanese GDPs, Bank of Japan Working Paper Series, No. 18-E-18.
Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistic for autoregressive time series with a unit root. Econometrica, 49(4), 1057–1072.
Exterkate, P., Groenen, P. J. F., Heij, C., & van Dijk, D. (2016). Nonlinear forecasting with many predictors using kernel ridge regression. International Journal of Forecasting, 32(3), 736–753.
Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22.
Giannone, D., Reichlin, L., & Small, D. (2008). Nowcasting: The real-time information content of macroeconomic data. Journal of Monetary Economics, 55, 665–676.
Hayakawa, K., & Kobayashi, Y. (2011). Business cycle analysis using a large-scale macro data. In: Quantitative Analysis of Finance and Business Cycle, Minerva Shobo, pp 91–111, in Japanese.
Kowarik, A., Meraner, A., & Templ, M. (2014). Seasonal adjustment with the R packages x12 and x12GUI. Journal of Statistical Software, 62(1), 1–21.
Li, J., & Chen, W. (2014). Forecasting macroeconomic time series: LASSO-based approach and their forecast combinations with dynamic factor models. International Journal of Forecasting, 30(4), 996–1015.
Ludvigson, S. C., & Ng, S. (2009). Macro factors in bond risk premia. Review of Finacial Studies, 22(12), 5027–5067.
Marsilli, C. (2014). Variable selection in predictive MIDAS models, Banque de France Working Paper.
Meier, L. (2015). grplasso: Fitting User Specified Models with Group Lasso Penalty. R package version 0.4-5.
Nicholson, W. B., Matteson, D. S., & Bien, J. (2017). VARX-L: Structured regularization for large vector autoregressions with exogenous variables. International Journal of Forecasting, 33(3), 627–651.
Onatski, A. (2010). Determing the number of factors from empirical distribution of eigenvalues. Review of Economics and Statistics, 92(4), 1004–1016.
Pfaff, B. (2008). Analysis of Integrated and Cointegrated Time Series with R. Berlin: Springer.
Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.
R Core Team (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, https://www.R-project.org/, vienna Austria.
Shibamoto, M. (2007). An analysis of monetary policy shocks in japan: A factor augumented vector autoregressive approach. Japanese Economic Review, 58(4), 484–503.
Shintani, M. (2005). Nonlinear forecasting analysis using diffusion indexes: An application to japan. Journal of Money, Credit and Banking, 37(3), 517–538.
Smeekes, S., & Wijler, E. (2018). Macroeconomic forecasting using penalized regression. International Journal of Forecasting, 34(3), 408–430.
Song, S., & Bickel, PJ. (2011). Large vector auto regressions, arXiv:1106.3915.
Stock, J. H., & Watson, M. W. (2002a). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97(460), 1167–1179.
Stock, J. H., & Watson, M. W. (2002b). Macroeconomic forecasting using diffusion indexes. Journal of Business & Economic Statistics, 20(2), 147–162.
Swanson, N. R., & Xiong, W. (2018). Big data analytics in economics: What have we learned so far, and where should we go from here? Canadian Journal of Economics, 51(3), 695–746.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B, 58(1), 267–288.
Uematsu, Y., & Tanaka, S. (2019). High-dimensional macroeconomic forecasting and variable selection via penalized regression. Econometrics Journal, 22, 34–56.
Yamamoto, Y. (2019). Bootstrap inference for impulse response functions in factor-augumented vector autoregressions. Journal of Applied Econometrics, 34(2), 247–267.
Yuan, M., & Lin, Y. (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society Series B, 68(1), 49–67.
Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society Series B, 67(2), 301–320.
Acknowledgements
We would like to thank Kazuhiko Hayakawa and Masahiko Shibamoto for their advice on creating our dataset. We also thank Shigeyuki Hamori, a co-editor, and two anonymous referees for their comments.
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Nakajima, Y., Sueishi, N. Forecasting the Japanese macroeconomy using high-dimensional data. JER 73, 299–324 (2022). https://doi.org/10.1007/s42973-020-00041-z
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DOI: https://doi.org/10.1007/s42973-020-00041-z