Seasonality and a Trend Dr Ron Lembke Washoe
Seasonality and a Trend Dr. Ron Lembke
Washoe Gaming Win, 1993 -96 What did they mean when they said it was down three quarters in a row? 1993 1994 1995 1996 Look at year-over-year
Seasonality • Seasonality is regular up or down movements in the data • Can be hourly, daily, weekly, yearly • Naïve method ▫ N 1: Assume January sales will be same as December ▫ N 2: Assume this Friday’s ticket sales will be same as last
Seasonal Factors • Seasonal factor for May is 1. 20, means May sales are typically 20% above the average • Factor for July is 0. 90, meaning July sales are typically 10% below the average
Seasonality & No Trend Spring Summer Fall Winter Total Avg Sales Factor 200/250 = 0. 8 350350/250 = 1. 4 300/250 = 1. 2 150/250 = 0. 6 1, 000/4=250 4. 0
Seasonal Factors • Compute average for each period • Compute overall average • Divide period averages by overall to get indexes. • Ok to have different # of data points
Seasonality & No Trend If we expected total demand for the next year to be 1, 100, the average per quarter would be 1, 100/4=275 Forecast Spring 275 * 0. 8 = 220 Summer 275 * 1. 4 = 385 Fall 275 * 1. 2 = 330 Winter 275 * 0. 6 = 165 Total 1, 100
Trend & Seasonality • Deseasonalize to find the trend 1. Calculate seasonal factors 2. Deseasonalize the demand 3. Find trend of deseasonalized line • Project trend into the future 4. Project trend line into future 5. Multiply trend line by seasonal component.
Seasonally Adjusting Unemployment, in Thousands, Unadjusted 155000 154000 153000 152000 151000 150000 Jan Mar May Jul Sep Nov Jan Mar May 149000 2009 2010 2011 2012 • Makes it easier to see trends BLS data, 2012 BLS report, 2012
Washoe Gaming Win, 1993 -96 Looks like a downhill slide -Silver Legacy opened 95 Q 3 -Otherwise, upward trend 1993 1994 1995 1996 Source: Comstock Bank, Survey of Nevada Business & Economics
Washoe Win 1989 -1996 Definitely a general upward trend, slowed 93 -94
1989 -2007 Red line shows “de-seasonalized” data
1989 -2007 Linear Regression
1998 -2007 Cache Creek 9/11 Thunder CC Valley Expands
Selecting Data • • What data to use? All of it? Representative? Overall upward trend 2000 -2003, downwards From 2003, fairly stable? From 2003 upward trend? The data you select to use has significant impact on the results you get and the conclusions you draw. ▫ Spend time making sure data are representative
2003 -2012 Data
2003 -2012 LR using 2008 Q 3 -2010 Q 4 R-squared = 0. 78
2011 Forecast using 2003 -10 SR 350, 000 300, 000 250, 000 200, 000 150, 000 Washoe Win 100, 000 Data for LR Linear Forecast 50, 000 2003 2004 2005 2006 2007 2008 2009 2010 2011 Seasonal Indexes calculated using 2003 -10 data
How Good Was It? Pattern fits data pretty well, but win better than expected.
1. Compute Seasonal Indexes Q 1 Q 2 Q 3 Q 4 2003 240, 114, 703 259, 349, 602 279, 784, 440 246, 068, 018 2004 231, 607, 546 259, 849, 383 297, 401, 507 259, 617, 607 2005 245, 793, 646 269, 238, 341 294, 810, 396 257, 014, 585 2006 245, 775, 176 269, 670, 481 294, 839, 349 257, 155, 338 2007 244, 648, 019 273, 460, 685 284, 733, 890 246, 352, 794 2008 227, 915, 101 237, 045, 466 258, 990, 669 206, 203, 166 2009 190, 098, 500 211, 913, 667 217, 227, 445 185, 971, 111 2010 187, 016, 132 198, 330, 968 209, 608, 491 175, 601, 589 2011 174, 138, 905 192, 122, 889 203, 912, 214 175, 510, 911 2012 175, 417, 340 241, 220, 165 260, 145, 378 223, 277, 235 Avg Indexes 216, 252, 507 0. 919 1. 025 1. 106 0. 949 235, 223, 821
2. Deseasonalize Year Quarter 2003 2004 1 2 3 4 Gaming Win 240, 114, 703 259, 349, 602 279, 784, 440 246, 068, 018 231, 607, 546 259, 849, 383 297, 401, 507 259, 617, 607 Seasonal 0. 919 1. 025 1. 106 0. 949 Deseas 261, 179, 391 252, 902, 590 252, 981, 489 259, 234, 039 251, 925, 921 253, 389, 947 268, 910, 866 273, 508, 607 Deseasonalize by dividing actual number by index Use same index value for All Q 1 s, same number for All Q 2 s, etc.
3. LR on Deseasonalized data 2008 Q 4 -2012 Q 1 Period 1 2 3 4 5 6 7 8 9 10 Deseasonalized 217, 236, 193 206, 775, 386 206, 645, 836 196, 417, 365 195, 921, 610 203, 422, 609 193, 400, 781 189, 528, 296 184, 997, 260 189, 415, 694 Intercept = 210, 576, 193 Slope = -2, 065, 456 R-squared = 0. 75
4. Project trend line into future Intercept = Slope = 210, 576, 193 -2, 065, 456
5. Multiply by Seasonal Relatives Linear Trend Period Q Line Seasonalized Relative Forecast 11 1 189, 789, 679 1. 025 194, 627, 812 12 2 186, 820, 177 1. 106 206, 613, 451 13 3 183, 850, 675 0. 949 174, 513, 237 14 4 180, 881, 173 0. 919 166, 292, 712
Final Forecast
Summary 1. Calculate indexes 2. Deseasonalize 1. Divide actual demands by seasonal indexes 3. Do a LR 4. Project the LR into the future 5. Seasonalize 1. Multiply straight-line forecast by indexes
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