Forecasting with a Trend Dr. Ron Lembke
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
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
Computing Values
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.
Trend-Adjusted Ex. Smoothing
Trend-Adjusted Ex. Smoothing Forecast including trend for period 1 is Suppose actual demand is 115, A1=115
Trend-Adjusted Ex. Smoothing Forecast including trend for period 2 is Suppose actual demand is 120, A2=120
FIT5=F5+T5 F6 A5 F5 Long’s Peak, CO, 14,259
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
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)
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!
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
Economist, Feb. 2011
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?
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%
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 2004/5 50-70% in first week Shrek 2: 12.1m in first 3 days Far Far Away Idol Had to vote in first week
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