Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles

This paper introduces five new univariate exponentially weighted methods for forecasting intraday time series that contain both intraweek and intraday seasonal cycles. Applications of relevance include forecasting volumes of call centre arrivals, transportation, e-mail traffic and electricity loads. The first method that we develop extends an exponential smoothing formulation that has been used for daily sales data, and which involves smoothing the total weekly volume and its split across the periods of the week. Two new methods are proposed that use discount weighted regression (DWR). The first uses DWR to estimate the time-varying parameters of a model with trigonometric terms. The second introduces DWR splines. We also consider a time-varying spline that uses exponential smoothing. The final new method presented here involves the use of singular value decomposition followed by exponential smoothing. Empirical results are provided using a series of intraday call centre arrivals.

[1]  Rob J. Hyndman,et al.  Forecasting time series with multiple seasonal patterns , 2008, Eur. J. Oper. Res..

[2]  D. Poirier.  Piecewise Regression Using Cubic Splines , 1973 .

[3]  Ashley D. Taylor.  Trade and Financial Sector Reforms: Interactions and Spillovers , 2010 .

[4]  Ralph D. Snyder,et al.  Forecasting intraday time series with multiple seasonal cycles using parsimonious seasonal exponential smoothing , 2009 .

[5]  Göran Kauermann,et al.  Functional hourly forecasting of water temperature , 2010 .

[6]  Haipeng Shen,et al.  FORECASTING TIME SERIES OF INHOMOGENEOUS POISSON PROCESSES WITH APPLICATION TO CALL CENTER WORKFORCE MANAGEMENT , 2008, 0807.4071.

[7]  James W. Taylor,et al.  Forecasting daily supermarket sales using exponentially weighted quantile regression , 2007, Eur. J. Oper. Res..

[8]  Avishai Mandelbaum,et al.  Telephone Call Centers: Tutorial, Review, and Research Prospects , 2003, Manuf. Serv. Oper. Manag..

[9]  James W. Taylor,et al.  A Comparison of Univariate Time Series Methods for Forecasting Intraday Arrivals at a Call Center , 2008, Manag. Sci..

[10]  Haipeng Shen,et al.  Interday Forecasting and Intraday Updating of Call Center Arrivals , 2008, Manuf. Serv. Oper. Manag..

[11]  J. W. Taylor,et al.  Short-term electricity demand forecasting using double seasonal exponential smoothing , 2003, J. Oper. Res. Soc..

[12]  W. R. Christiaanse.  Short-Term Load Forecasting Using General Exponential Smoothing , 1971 .

[13]  Rob J. Hyndman,et al.  Robust forecasting of mortality and fertility rates: A functional data approach , 2007, Comput. Stat. Data Anal..

[14]  P. Young,et al.  Dynamic harmonic regression. , 1999 .

[15]  Ta-Hsin Li,et al.  On Exponentially Weighted Recursive Least Squares for Estimating Time-Varying Parameters and its Application to Computer Workload Forecasting , 2008 .

[16]  Melvin J. Hinich,et al.  Detecting intraday periodicities with application to high frequency exchange rates , 2001 .

[17]  P. J. Harrison,et al.  Discount Weighted Regression , 1984 .

[18]  Jonathan Weinberg,et al.  Bayesian Forecasting of an Inhomogeneous Poisson Process With Applications to Call Center Data , 2007 .

[19]  P. McSharry,et al.  Short-Term Load Forecasting Methods: An Evaluation Based on European Data , 2007, IEEE Transactions on Power Systems.

[20]  A. Harvey,et al.  Forecasting Hourly Electricity Demand Using Time-Varying Splines , 1993 .

[21]  Robert Goodell Brown,et al.  Smoothing, forecasting and prediction of discrete time series , 1964 .

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

[23]  P. J. Harrison,et al.  Discount weighted estimation , 1984 .

[24]  Diego J. Pedregal,et al.  An unobserved component model for multi-rate forecasting of telephone call demand: the design of a forecasting support system , 2002 .

[25]  Yf F. Tang,et al.  Short-term Hourly Traffic Forecasts using Hong Kong Annual Traffic Census , 2006 .

[26]  Philippe Vieu,et al.  Nonparametric time series prediction: A semi-functional partial linear modeling , 2008 .

[27]  Haipeng Shen,et al.  Analysis of call centre arrival data using singular value decomposition , 2005 .

[28]  Kurt M. Bretthauer,et al.  Real-Time Work Schedule Adjustment Decisions: An Investigation and Evaluation , 2009 .

[29]  Rob J Hyndman,et al.  Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing , 2011 .

[30]  P. McSharry,et al.  A comparison of univariate methods for forecasting electricity demand up to a day ahead , 2006 .

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

[32]  Andrea Liverani,et al.  Climate Change and Individual Behavior: Considerations for Policy , 2009 .

[33]  James W. Taylor,et al.  Density Forecasting of Intraday Call Center Arrivals Using Models Based on Exponential Smoothing , 2012, Manag. Sci..

[34]  John Foster,et al.  Randomly Modulated Periodic Signals in Australias National Electricity Market , 2008 .