Seasonality and a TrendDr. Ron Lembke
Washoe Gaming Win, 1993-96
180
200
220
240
260
280
300
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
What did they mean when they said it was down three quartersin a row?
1993 1994 1995 1996
Look atyear-over-year
Seasonality•Seasonality is regular up or down
movements in the data•Can be hourly, daily, weekly, yearly•Naïve method
▫N1: Assume January sales will be same as December
▫N2: 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 TrendSales Factor
Spring 200 200/250 = 0.8Summer 350 350/250 = 1.4Fall 300 300/250 = 1.2Winter 150 150/250 = 0.6
Total 1,000 4.0Avg 1,000/4=250
Seasonal Factors1 2 3 Average Index
Jan 90 95 92.5 0.4803Feb 95 89 92.0 0.4777Mar 158 169 155 160.7 0.8342Apr 240 220 235 231.7 1.2029May 250 240 225 238.3 1.2375Jun 310 300 313 307.7 1.5975Jul 380 400 420 400.0 2.0769Aug 340 350 320 336.7 1.7480Sep 135 140 150 141.7 0.7356Oct 105 100 90 98.3 0.5106Nov 80 70 65 71.7 0.3721Dec 130 150 140.0 0.7269
Avg 192.6 12
Year
• Compute average for each period
• Compute overall average• Divide period averages by
overall to get indexes.• Ok to have different # of
data points
050
100150200250300350400450
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1
2
3
Seasonality & No TrendIf we expected total demand for the next
year to be 1,100, the average per quarter would be 1,100/4=275
ForecastSpring 275 * 0.8 = 220Summer 275 * 1.4 = 385Fall 275 * 1.2 = 330Winter 275 * 0.6 = 165Total 1,100
Trend & Seasonality• Deseasonalize to find the trend
1. Calculate seasonal factors2. Deseasonalize the demand3. Find trend of deseasonalized line
• Project trend into the future4. Project trend line into future5. Multiply trend line by seasonal component.
Seasonally AdjustingJa
nFe
bM
ar Apr
May Jun Jul
Aug
Sep
Oct
Nov
Dec Jan
Feb
Mar Apr
May Jun Jul
Aug
Sep
Oct
Nov
Dec Jan
Feb
Mar Apr
May Jun Jul
Aug
Sep
Oct
Nov
Dec Jan
Feb
Mar Apr
May Jun Jul
Aug
Sep
Oct
Nov
Dec
2009 2010 2011 2012
149000
150000
151000
152000
153000
154000
155000
Une
mpl
oym
ent,
in T
hous
ands
, Una
d-ju
sted
BLS report, 2012
•Makes it easier to see trends
BLS data, 2012
Washoe Gaming Win, 1993-96
180
200
220
240
260
280
300
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
Looks like a downhill slide- Silver Legacy
opened 95Q3- Otherwise,
upward trend
1993 1994 1995 1996
Source: Comstock Bank, Survey of Nevada Business & Economics
Washoe Win 1989-1996
150000
170000
190000
210000
230000
250000
270000
290000
1989 1990 1991 1992 1993 1994 1995 1996
Definitely a general upward trend, slowed 93-94
1989-2007
Red line shows “de-seasonalized” data
1989-2007 Linear Regression
1998-2007
CacheCreek
ThunderValley
CCExpands
9/11
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 2008Q3-2010Q4
R-squared = 0.78
2003 2004 2005 2006 2007 2008 2009 2010 2011 -
50,000,000
100,000,000
150,000,000
200,000,000
250,000,000
300,000,000
350,000,000
Washoe Win
Linear
Forecast
2011 Forecast using 2003-10 SR
Data for LR
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
Q1 Q2 Q3 Q4
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
Avg 216,252,507 241,220,165 260,145,378 223,277,235 235,223,821
Indexes 0.919 1.025 1.106 0.949
2.DeseasonalizeYear Quarter Gaming Win Seasonal Deseas
2003 1 240,114,703 0.919 261,179,391 2 259,349,602 1.025 252,902,590 3 279,784,440 1.106 252,981,489 4 246,068,018 0.949 259,234,039
2004 1 231,607,546 0.919 251,925,921 2 259,849,383 1.025 253,389,947 3 297,401,507 1.106 268,910,866 4 259,617,607 0.949 273,508,607
Deseasonalize by dividing actual number by indexUse same index value for All Q1s, same number forAll Q2s, etc.
3.LR on Deseasonalized data 2008 Q4-2012Q1
Period Deseasonalized1 217,236,193
2 206,775,386
3 206,645,836
4 196,417,365
5 195,921,610
6 203,422,609
7 193,400,781
8 189,528,296
9 184,997,260
10 189,415,694
Intercept = 210,576,193Slope = -2,065,456R-squared =0.75
4.Project trend line into future
Intercept = 210,576,193Slope = -2,065,456
5.Multiply by Seasonal RelativesPeriod Q
Linear Trend Line
Seasonal Relative
Seasonalized 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
Summary1. Calculate indexes2. Deseasonalize
1. Divide actual demands by seasonal indexes
3. Do a LR4. Project the LR into the future5. Seasonalize
1. Multiply straight-line forecast by indexes
Top Related