Forecasting with a Trend

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 • “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 Aldrinvideo (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

15. 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? Dangers of Historical Analogies

16. 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%

17. Lessons Learned • Guaranteed Sales: flooded market with DVDs • 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 • 2004/5 50-70% in first week • Shrek 2: 12.1m in first 3 days • Far Far Away Idol • Had to vote in first week

18. 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