High-dimensional Holt-Winters trend model: Fast estimation and prediction

References

• Akaike, H. (1980). Seasonal adjustment by a bayesian modeling. In Selected papers of Hirotugu Akaike (pp. 333–345). Berlin, Germany: Springer.
   Google Scholar
• Athanasopoulos, G., Hyndman, R. J., Kourentzes, N., & Petropoulos, F. (2017). Forecasting with temporal hierarchies. European Journal of Operational Research, 262(1), 60–74. doi:10.1016/j.ejor.2017.02.046
   Web of Science ®Google Scholar
• Bell, W., & Hillmer, S. (1991). Initializing the kalman filter for nonstationary time series models. Journal of Time Series Analysis, 12(4), 283–300. doi:10.1111/j.1467-9892.1991.tb00084.x
   Google Scholar
• Bermúdez, J. D., Segura, J. V., & Vercher, E. (2006). Improving demand forecasting accuracy using nonlinear programming software. Journal of the Operational Research Society, 57(1), 94–100. doi:10.1057/palgrave.jors.2601941
   Web of Science ®Google Scholar
• Bermúdez, J. D., Segura, J. V., & Vercher, E. (2010). Bayesian forecasting with the holt–winters model. Journal of the Operational Research Society, 61(1), 164–171. doi:10.1057/jors.2008.152
   Web of Science ®Google Scholar
• Box, G. E., & Jenkins, G. M. (1976). Time series analysis: forecasting and control, revised ed. San Francisco, CA: Holden-Day.
   Google Scholar
• Carvalho, V. M., & Harvey, A. C. (2005). Convergence in the trends and cycles of euro-zone income. Journal of Applied Econometrics, 20(2), 275–289. doi:10.1002/jae.820
   Web of Science ®Google Scholar
• Cornea-Madeira, A. (2017). The explicit formula for the Hodrick-Prescott filter in a finite sample. The Review of Economics and Statistics, 99(2), 314–318. doi:10.1162/REST_a_00594
   Web of Science ®Google Scholar
• Dermoune, A., Djehiche, B., & Rahmania, N. (2009). Multivariate extension of the Hodrick-Prescott filter-optimality and characterization. Studies in Nonlinear Dynamics & Econometrics, 13(3), 4. doi:10.2202/1558-3708.1656
   Web of Science ®Google Scholar
• Diebold, F. X., & Mariano, R. S. (1995). Comparing predictive accuracy. Journal of Business & Economic Statistics, 13(3), 253–263. doi:10.2307/1392185
   Web of Science ®Google Scholar
• Durbin, J., & Koopman, S. J. (2012). Time series analysis by state space methods. Oxford, UK: Oxford University Press.
   Google Scholar
• Eddelbuettel, D., & Sanderson, C. (2014). Rcpparmadillo: Accelerating r with high-performance c++ linear algebra. Computational Statistics & Data Analysis, 71, 1054–1063. doi:10.1016/j.csda.2013.02.005
   Web of Science ®Google Scholar
• Hamilton, J. D. (2018). Why you should never use the Hodrick-Prescott filter. The Review of Economics and Statistics, 100(5), 831–843. doi:10.1162/rest_a_00706
   Web of Science ®Google Scholar
• Harvey, A. (1986). Analysis and generalisation of a multivariate exponential smoothing model. Management Science, 32(3), 374–380. doi:10.1287/mnsc.32.3.374
   Web of Science ®Google Scholar
• Harvey, A. C. (1989). Forecasting, structural time series analysis, and the kalman filter. Cambridge: Cambridge University Press.
   Google Scholar
• Harvey, D., Leybourne, S., & Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of Forecasting, 13(2), 281–291. doi:10.1016/S0169-2070(96)00719-4
   Web of Science ®Google Scholar
• Henderson, R. (1924). A new method of graduation. Transactions of the Actuarial Society of America, 25, 29–40.
   Google Scholar
• Holt Charles, C. (2004). Forecasting trends and seasonal by exponentially weighted averages. International Journal of Forecasting, 20(1), 5–10. doi:10.1016/j.ijforecast.2003.09.015
   Web of Science ®Google Scholar
• Hyndman, R., Koehler, A. B., Ord, J. K., & Snyder, R. D. (2008). Forecasting with exponential smoothing: the state space approach. Berlin, Germany: Springer Science & Business Media.
   Google Scholar
• Jonsson, K. (2018). Extending the state-space representation of the judgement-augmented Hodrick-Prescott filter. Economics Bulletin, 38(1), 623–628.
   Web of Science ®Google Scholar
• Kaiser, R., & Maravall, A. (2001). Measuring business cycles in economic statistics. In Lecture Notes in Statistics, Vol. 154. New York: Springer-Verlag
   Google Scholar
• Kitagawa, G. (1981). A nonstationary time series model and its fitting by a recursive filter. Journal of Time Series Analysis, 2(2), 103–116. doi:10.1111/j.1467-9892.1981.tb00316.x
   Google Scholar
• Kitagawa, G., & Gersch, W. (1984). A smoothness priors–state space modeling of time series with trend and seasonality. Journal of the American Statistical Association, 79(386), 378–389. doi:10.2307/2288279
   Web of Science ®Google Scholar
• Koopman, S. J. (1993). Disturbance smoother for state space models. Biometrika, 80 (1), 117–126. doi:10.1093/biomet/80.1.117
   Web of Science ®Google Scholar
• Leser, C. (1961). A simple method of trend construction. Journal of the Royal Statistical Society: Series B (Methodological)), 23 (1), 91–107. doi:10.1111/j.2517-6161.1961.tb00393.x
   Google Scholar
• Maravall, A., & Río, A. D. (2007). Temporal aggregation, systematic sampling, and the Hodrick–Prescott filter. Computational Statistics & Data Analysis, 52(2), 975–998. doi:10.1016/j.csda.2007.08.001
   Web of Science ®Google Scholar
• Mathematica, W. (2012). version 9.0. 1.0. Wolfram Research Inc.
   Google Scholar
• McElroy, T., & Trimbur, T. (2015). Signal extraction for non-stationary multivariate time series with illustrations for trend inflation. Journal of Time Series Analysis, 36(2), 209–227. doi:10.1111/jtsa.12102
   Web of Science ®Google Scholar
• Mills, T., & Patterson, K. (2015). Modelling the trend: The historical origins of some modern methods and ideas. Journal of Economic Surveys, 29(3), 527–548. doi:10.1111/joes.12073
   Web of Science ®Google Scholar
• Ord, K., Fildes, R. A., & Kourentzes, N. (2017). Principles of business forecasting. Wessex Press Publishing Co.
   Google Scholar
• Pelagatti, M. M. (2015). Time series modelling with unobserved components. Boca Raton, FL: CRC Press.
   Google Scholar
• Pennings, C. L., & Dalen, J. V. (2017). Integrated hierarchical forecasting. European Journal of Operational Research, 263(2), 412–418. doi:10.1016/j.ejor.2017.04.047
   Web of Science ®Google Scholar
• Petropoulos, F., Makridakis, S., Assimakopoulos, V., & Nikolopoulos, K. (2014). horses for courses in demand forecasting. European Journal of Operational Research, 237(1), 152–163. doi:10.1016/j.ejor.2014.02.036
   Web of Science ®Google Scholar
• Poloni, F., & Sbrana, G. (2016). Multivariate trend-cycle extraction with the Hodrick-Prescott filter. Macroeconomic Dynamics, 21, 1336–1360. doi:10.1017/S1365100515000887
   Web of Science ®Google Scholar
• Proietti, T. (2009). Structural time series models for business cycle analysis. In Palgrave handbook of econometrics (pp. 385–433). Berlin, Germany: Springer.
   Google Scholar
• Sbrana, G., Silvestrini, A., & Venditti, F. (2017). Short-term inflation forecasting: The meta approach. International Journal of Forecasting, 33(4), 1065–1081. doi:10.1016/j.ijforecast.2017.06.007
   Web of Science ®Google Scholar
• Shumway, R. H., & Stoffer, D. S. (1982). An approach to time series smoothing and forecasting using the em algorithm. Journal of Time Series Analysis, 3(4), 253–264. doi:10.1111/j.1467-9892.1982.tb00349.x
   Google Scholar
• Taylor, J. W. (2003). Short-term electricity demand forecasting using double seasonal exponential smoothing. Journal of the Operational Research Society, 54(8), 799–805. doi:10.1057/palgrave.jors.2601589
   Web of Science ®Google Scholar
• Theil, H., & Wage, S. (1964). Some observations on adaptive forecasting. Management Science, 10(2), 198–206. doi:10.1287/mnsc.10.2.198
   Web of Science ®Google Scholar
• Whittaker, E. T. (1922). On a new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41, 63–75. doi:10.1017/S0013091500077853
   Google Scholar
• Williams, T. (1987). Adaptive holtwinters forecasting. The Journal of the Operational Research Society, 38(6), 553–560. doi:10.2307/2582769
   Web of Science ®Google Scholar
• Winters, P. R. (1960). Forecasting sales by exponentially weighted moving averages. Management Science, 6(3), 324–342. doi:10.1287/mnsc.6.3.324
   Web of Science ®Google Scholar
• Yamada, H. (2018). Why does the trend extracted by the Hodrick–Prescott filtering seem to be more plausible than the linear trend?. Applied Economics Letters, 25(2), 102–105. doi:10.1080/13504851.2017.1299095
   Web of Science ®Google Scholar