TRUCK FORECASTING WITH TIME SERIES …

1 TRUCK FORECASTING with time SERIES analysis : A CASE STUDY OF THE BLUE WATER BRIDGE University of Wisconsin Milwaukee Paper No. 11-5 National Center for Freight & Infrastructure Research & Education College of Engineering Department of Civil and Environmental Engineering University of Wisconsin, Madison Authors: Jing Mao and Alan J. Horowitz Center for Urban Transportation Studies University of Wisconsin Milwaukee Principal Investigator: Alan J. Horowitz Professor, Civil Engineering and Mechanics Department, University of Wisconsin Milwaukee December 22, 2011 TRUCK FORECASTING with time SERIES analysis : A Case Study of the Blue Water Bridge INTRODUCTION This document contains images of all slides in a course module about the use of time SERIES techniques for TRUCK FORECASTING .

2 The techniques are illustrated with data from the Blue Water Bridge between Michigan and Ontario. This presentation is available upon request to Alan Horowitz, 12/22/20111 TRUCK FORECASTING with time SERIES analysis : A Case Study of the Blue Water BridgePrepared by Jing MaoAlan J. HorowitzOutline Introduction Data Collection Methodology Conclusion 12/22/20112 Blue Water Bridge LocationThe Blue Water Bridge spans the Saint Clair River, and carries international traffic between Port Huron, Michigan and Point Edward and Sarnia, Ontario.

3 Located near interchange of I-94 and I-69, the bridge forms a critical gateway linking Canada and the United characteristics The original Blue Water Bridge, opened in 1938 and renovated in 1999, is a three-lane westbound bridge. The second Blue Water Bridge, which carries three lanes of eastbound traffic, is an impressive modern bridge opened in Water Bridge 12/22/20113 Purpose of the Study FORECASTING the eastbound and westbound monthly TRUCK volume of blue water bridge from 2011 to 2013 Applying the different time SERIES models and select the best one for FORECASTING Data Source Dependent variables Independent variables oMichigan population (why freight moves)oOntario population (why freight moves) GDP and population (why freight moves)

4 OApproximate Michigan GDP (derived from GDP by the proportion of Michigan population and population) all grades all formulations retail gasoline fuel price (major cost of freight)oNorth American Free Trade Agreement (NAFTA) (why freight moves)oSeptember 11 attacks (why freight does not move)Blue water bridge eastbound/ westbound TRUCK volume 12/22/20114 Descriptive Statistic of Dependent Variables Westbound and eastbound TRUCK volume data from Jan 1984 to Dec 2010 by each month 050001000015000200002500030000 Jan-84 Jun-84 Nov-84 Apr-85 Sep-85 Feb-86 Jul-86 Dec-86 May-87 Oct-87 Westbound Westbound050001000015000200002500030000 Jan-84 Jun-84 Nov-84 Apr-85 Sep-85 Feb-86 Jul-86 Dec-86 May-87 Oct-87 EastboundEastboundWestbound TRUCK volume from Jan 1984 to Dec 1987 Eastbound TRUCK volume from Jan 1984 to Dec 1987

5 Michigan and Ontario population data from Jan 1984 to Dec 2010 by each month Descriptive Statistic of Independent Variables Population(million)OntarioPopulation( Population(million) Michigan12/22/20115 US GDP data from Jan 1984 to Dec 2010 by each month and yearly population data GDP US GDP(billion)US GDP(billion) Population (million)PopulationDescriptive Statistic of Independent Variables Computing the ratio of Michigan population and population Computing Michigan GDP by applying the ratio to Michigan GDP and GDP Approximate Michigan GDPR atio = Michigan population / populationMichigan GDP = Ratio * GDP12/22/20116 Michigan GDP data and all grades all formulations retail gasoline fuel price data from Jan 1984 to Dec 2010 by each month price All Grades All Formulations Retail Gasoline fuel Price (Dollar per Gallon based current year))

6 All GradesAll FormulationsRetail Gasolinefuel GDP(billion)MichiganGDP(billion)Descript ive Statistic of Independent Variables Other Data NAFTAoThe North American Free Trade Agreement or NAFTA is an agreement signed by the governments ofCanada,Mexico, and theUnited States, creating a trilateraltrade blocin North America. The agreement came into force on January 1, 1994. It superseded theCanada United States Free Trade Agreementbetween the and Canada. September 11 oThe September 11 attacks could also be a factor to influence the TRUCK volume within that SERIES Models Central Moving Average Growth Factor Exponential Smoothing Linear Regression ARIMAoBox-Cox TransformationCentral Moving AverageGrowth FactorExponential SmoothingLinear RegressionARIMAC entral Moving Average Central moving average is a moving average such that time period is at the center of the N time periods used to determine which values to average.

7 12/22/20118 Westbound and Eastbound moving average data fromJul 1984 to Aug 2010010000200003000040000500006000070000 8000090000 Jul-84 Dec-86 May-89 Oct-91 Mar-94 Aug-96 Jan-99 Jun-01 Nov-03 Apr-06 Sep-08 TRUCK VolumeEastbound Moving AverageSeries1 Series2010000200003000040000500006000070 0008000090000100000 Jul-84 Jun-87 May-90 Apr-93 Mar-96 Feb-99 Jan-02 Dec-04 Nov-07 TRUCK VolumeWestbound Moving AverageSeries1 Series2R square square Moving Average Seasonal adjustment factor can be used to improve accuracy of TRUCK volume forecastsSeasonal adjustment factor12/22/20119 Growth FactorLinear growth:F(n) = Constant + AGF * (n)F(n): forecast volume AGF: average growth factorn: the number of months from the first observationGrowth Factor Determination of constant and AGF from the linear regressionoTools / Add-ins / analysis Tool ParkoTools / Data analysis / RegressionoIndependent variable: monthoDependent variable: westbound TRUCK volume (partial initial data)Constant:13767 AGF.

8 11912/22/201110F(n)=13767+119*nGrowth Factor ForecastingPartial results with growth factor forecastingForecasting Results with All Initial DataR Square VolumeWestbound FORECASTING Actual dataForecasted dataR Square VolumeEastbound ForecastingActual dataForecasted data12/22/201111 Growth Factor FORECASTING with Central Moving Average SERIES F(n)=14291+230*nPartial central moving average TRUCK volume Partial central moving average SERIES R Square VolumeWestbound ForecastingMoving AverageForecasting0100002000030000400005 0000600007000080000 Sep-84 Jan-86 May-87 Sep-88 Jan-90 May-91 Sep-92 Jan-94 May-95 Sep-96 Jan-98 May-99 Sep-00 Jan-02 May-03 Sep-04 Jan-06 May-07 Sep-08 Jan-10 May-11 TRUCK VolumeEastbound ForecastingMoving AverageForecastingR Square Results with All Smoothed Data12/22/201112 Comparing R Square of Growth factor with initial data and moving

9 Average(smoothed) dataComparisonR SquareInitial dataMoving average dataWestbound Compound growthF(n)=Constant*AGF(n)oIf there are two yearsWhere F1is the freight flow in year Y1, F2is the freight flow in year Y2oIf there are more than two years, AGF can be found from the linear regressionGrowth Factor12112 YYFFAGF =12/22/201113 Growth Factor Determination of constant and AGF from the linear regressionoTools / Add-ins / analysis Tool ParkoTools / Data analysis / RegressionoIndependent variable: monthoDependent variable: westbound TRUCK volume expressed as natural logarithm (partial initial data)oConstant = EXP (intercept) AGF = EXP (x-variable coefficient)Constant:13745 AGF: Factor ForecastingPartial results with compound regression FORECASTING F(n)= 13745* Model formulation:whereSt: exponentially smoothed value for time period tSt-1: exponentially smoothed value for time period t-1xt-1 : actual time SERIES value for time period t.

10 Thesmoothing factor, and 0 < <1 Exponential Smoothing *12878+ *13253 = + ( )St-112/22/201115 Smoothing factor oThe larger is, the closer the smoothed value will track the original data value. The smaller is, the more fluctuation is smoothed out. The determination of smoothing factoroGraph fitting oMean squared error (MSE) Smoothing factor assumed ( , , )Exponential