1. Forecasting with a Trend
Dr. Ron Lembke

2. Averaging Methods Simple Average Moving Average
Weighted Moving Average
Exponentially Weighted Moving Average (Exponential Smoothing)
They ALL take an average of the past
With a trend, all do badly
Average must be in-between 30 20 10

3. Linear Regression?
Determine how demand increases as a function of time
t = periods since beginning of data
b = Slope of the line
a = Value of yt at t = 0

4. Computing Values

5. Linear Regression Four methods
Type in formulas for trend, intercept
Tools | Data Analysis | Regression
Graph, and R click on data, add a trendline, and display the equation.
Use intercept(Y,X), slope(Y,X) and RSQ(Y,X) commands
R2 measures the percentage of change in y that can be explained by changes in x.
Gives all data equal weight.
Exp. smoothing with a trend gives more weight to recent, less to old.

6. Trend-Adjusted Ex. Smoothing

7. Trend-Adjusted Ex. Smoothing
Forecast including trend for period 1 is
Suppose actual demand is 115, A1=115

8. Trend-Adjusted Ex. Smoothing
Forecast including trend for period 2 is
Suppose actual demand is 120, A2=120

9. FIT5=F5+T5 F6 A5 F5
Long’s Peak, CO, 14,259

10. Selecting  and  You could:
Try an initial value for each parameter.
Try lots of combinations and see what looks best.
But how do we decide “what looks best?”
Let’s measure the amount of forecast error.
Then, try lots of combinations of parameters in a methodical way.
Let  = 0 to 1, increasing by 0.1
For each  value, try  = 0 to 1, increasing by 0.1

11. Another Analogy Hitting moon reflectors Ridiculously Simplified:
“Lunar Laser Ranging Exp”
Ridiculously Simplified:
Suppose know your location, and the proper angle
Error in location, miss target by few feet
Error in angle, miss the moon
Make small adjustments to trend
Buzz Aldrin video (age 72)

12. Projecting Further Into Future
F is our best guess, currently of the level
T is our best guess of growth rate
Boss asks for period 15.
Come back after period 14?
No!

13. Causal Forecasting
Linear regression seeks a linear relationship between the input variable and the output quantity.
For example, furniture sales correlates to housing sales
Not easy, multiple sources of error:
Understand and quantify relationship
Someone else has to forecast the x values for you

14. Economist, Feb. 2011

16. Dangers of Historical Analogies
Shrek did $500m at the box office, and sold almost 50 million DVDs & videos
Shrek2 did $920m at the box office
What will be the video sales?

17. Video sales of Shrek 2? Assume 1-1 ratio:
920/500 = 1.84
1.84 * 50 million = 92 million videos?
Fortunately, not that dumb.
January 3, 2005: 37 million sold!
March analyst call: 40m by end Q1
March SEC filing: 33.7 million sold. Oops.
May 10 Announcement:
In 2nd public Q, missed earnings targets by 25%.
May 9, word started leaking
Stock dropped 16.7%

18. Lessons Learned Guaranteed Sales: flooded market with DVDs 5 years ago
Promised the retailer they would sell them, or else the retailer could return them
Didn’t know how many would come back
5 years ago
Typical movie 30% of sales in first week
Animated movies even lower than that
2004/ % in first week
Shrek 2: 12.1m in first 3 days
Far Far Away Idol
Had to vote in first week

19. Summary Including a trend
Linear Regression gives equal weight to all data
FIT includes a trend, gives more weight to more recent data
Can predict more than one period into future
Causal relationships require estimating input numbers and relationships
Past history very helpful in predicting
But not perfect. Be aware of your assumptions