Improving forecasting by estimating time series structural components across multiple frequencies

Identifying the most appropriate time series model to achieve a good forecasting accuracy is a challenging task. We propose a novel algorithm that aims to mitigate the importance of model selection, while increasing the accuracy. Multiple time series are constructed from the original time series, using temporal aggregation. These derivative series highlight different aspects of the original data, as temporal aggregation helps in strengthening or attenuating the signals of different time series components. In each series, the appropriate exponential smoothing method is fitted and its respective time series components are forecast. Subsequently, the time series components from each aggregation level are combined, then used to construct the final forecast. This approach achieves a better estimation of the different time series components, through temporal aggregation, and reduces the importance of model selection through forecast combination. An empirical evaluation of the proposed framework demonstrates significant improvements in forecasting accuracy, especially for long-term forecasts.

[1]  A. Timmermann.  Chapter 4 Forecast Combinations , 2006 .

[2]  S. Kolassa.  Combining exponential smoothing forecasts using Akaike weights , 2011 .

[3]  Changzheng He,et al.  Combination of forecasts using self-organizing algorithms , 2005 .

[4]  William W. S. Wei,et al.  Time series analysis - univariate and multivariate methods , 1989 .

[5]  Rob J. Hyndman,et al.  Forecasting with Exponential Smoothing , 2008 .

[6]  Arnold Zellner,et al.  To combine or not to combine? Issues of combining forecasts , 1992 .

[7]  Clive W. J. Granger,et al.  Implications of seeing economic variables through an aggregation window , 1993 .

[8]  Fotios Petropoulos,et al.  An aggregate–disaggregate intermittent demand approach (ADIDA) to forecasting: an empirical proposition and analysis , 2011, J. Oper. Res. Soc..

[9]  J. Boylan,et al.  The accuracy of intermittent demand estimates , 2005 .

[10]  A. Timmermann.  Forecast Combinations , 2005 .

[11]  James W. Taylor.  Exponential smoothing with a damped multiplicative trend , 2003 .

[12]  Michael P. Clements,et al.  An Overview of Economic Forecasting , 2007 .

[13]  C. Granger,et al.  Handbook of Economic Forecasting , 2006 .

[14]  John E. Boylan,et al.  Forecast horizon aggregation in integer autoregressive moving average (INARMA) models , 2012 .

[15]  R. Clemen.  Combining forecasts: A review and annotated bibliography , 1989 .

[16]  Bovas Abraham,et al.  Temporal Aggregation and Time Series , 1982 .

[17]  Spyros Makridakis,et al.  The M3-Competition: results, conclusions and implications , 2000 .

[18]  K. Nikolopoulos,et al.  The theta model: a decomposition approach to forecasting , 2000 .

[19]  C. Hafner.  Temporal aggregation of multivariate GARCH processes , 2004 .

[20]  Ruud H. Teunter,et al.  Forecasting intermittent demand , 2006 .

[21]  Konstantinos Nikolopoulos,et al.  The Tourism Forecasting Competition , 2011 .

[22]  Rob J Hyndman,et al.  25 years of time series forecasting , 2006 .

[23]  T. Evgeniou,et al.  To combine or not to combine: selecting among forecasts and their combinations , 2005 .

[24]  Amir F. Atiya,et al.  Combination of long term and short term forecasts, with application to tourism demand forecasting , 2011 .

[25]  David Veredas,et al.  Temporal Aggregation of Univariate and Multivariate Time Series Models: A Survey , 2008 .

[26]  M C Hughes.  Forecasting practice: organisational issues , 2001, J. Oper. Res. Soc..

[27]  J. M. Bates,et al.  The Combination of Forecasts , 1969 .

[28]  K. Brewer.  Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models , 1973 .

[29]  Fotios Petropoulos,et al.  Improving the Performance of Popular Supply Chain Forecasting Techniques , 2011 .

[30]  R. L. Winkler,et al.  Averages of Forecasts: Some Empirical Results , 1983 .

[31]  James W. Taylor.  Exponentially Weighted Information Criteria for Selecting Among Forecasting Models , 2008 .

[32]  Takeshi Amemiya,et al.  The Effect of Aggregation on Prediction in the Autoregressive Model , 1972 .

[33]  Robert L. Winkler,et al.  The effect of nonstationarity on combined forecasts , 1992 .

[34]  M. Z. Babai,et al.  Impact of temporal aggregation on stock control performance of intermittent demand estimators: Empirical analysis , 2012 .

[35]  Philip Hans Franses,et al.  The M3 competition: Statistical tests of the results , 2005 .

[36]  Rob J Hyndman,et al.  Another look at measures of forecast accuracy , 2006 .

[37]  Robert L. Winkler,et al.  The accuracy of extrapolation (time series) methods: Results of a forecasting competition , 1982 .

[38]  Rob J Hyndman,et al.  A state space framework for automatic forecasting using exponential smoothing methods , 2002 .

[39]  T. Nijman,et al.  Temporal Aggregation of GARCH Processes. , 1993 .

[40]  R. Fildes,et al.  The Impact of Empirical Accuracy Studies On Time Series Analysis and Forecasting , 1995 .

[41]  Jeremy P. Smith,et al.  Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study , 2004 .

[42]  T. Willemain,et al.  Forecasting intermittent demand in manufacturing: a comparative evaluation of Croston's method , 1994 .

[43]  Robert L. Winkler,et al.  Simple robust averages of forecasts: Some empirical results , 2008 .

[44]  Miguel Jerez,et al.  Modelling and forecasting time series sampled at different frequencies , 2009 .

[45]  Rob J Hyndman,et al.  Forecasting with Exponential Smoothing: The State Space Approach , 2008 .

[46]  E. S. Gardner.  EXPONENTIAL SMOOTHING: THE STATE OF THE ART, PART II , 2006 .

[47]  Rob J Hyndman,et al.  Automatic Time Series Forecasting: The forecast Package for R , 2008 .

[48]  Fotios Petropoulos,et al.  A systemic view of the ADIDA framework , 2014 .

[49]  Steven C. Hillmer,et al.  A Benchmarking Approach to Forecast Combination , 1989 .

[50]  C. E. Agnew,et al.  Bayesian consensus forecasts of macroeconomic variables , 1985 .

[51]  Everette S. Gardner,et al.  Exponential smoothing: The state of the art , 1985 .

[52]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[53]  A. A. Weiss.  Systematic sampling and temporal aggregation in time series models , 1984 .

[54]  Pierre A. Cholette.  Prior Information and ARIMA Forecasting , 1982 .

[55]  Víctor Gómez,et al.  Programs TRAMO and SEATS, Instruction for User (Beta Version: september 1996) , 1996 .