1. FORECASTING

2. Types of Forecasts Qualitative Time Series Causal Relationships Simulation

3. Qualitative Forecasting Approaches Historical Analogy Panel Consensus Delphi Market Research

4. Quantitative Approaches Naïve (time series) Moving Averages (time series) Exponential Smoothing (time series) Trend Projection (time series) Linear Regression (causal)

5. Naïve Method This period’s forecast = Last period’s observation Crude but effective August sales = 1000; September sales = ?? 1000!

6. Moving Averages This period’s forecast = Average of past n period’s observations Example: for n = 3: Sales for Jan through March were 100, 110, 150 April forecast = (100+110+150)/3 = 120

7. Example

8. Evaluating Forecasts Concept: Forecast worth function of how close forecasts are to observations Mean Absolute Deviation (MAD) MAD = sum of absolute value of forecast errors / number of forecasts (e.g. periods) äMAD is the average of the absolute value of all of the forecast errors.

9. Weighted Moving Averages This period’s forecast = Weighted average of past n period’s observations Example: for n = 3: Sales for Jan through March were 100, 110, 150 Suppose weights for last 3 periods are:.5 (March),.3 (Feb), and.2 (Jan) April forecast =.5*150+.3*110+.2*100 = 128

10. Exponential Smoothing New Forecast = Last period’s forecast + alpha * (Last period’s actual observation - last period’s forecast) Mathematically: F(t) = F(t-1) + alpha * [A(t-1) - F(t-1)], where F is the forecast; A is the actual observation, and alpha is the smoothing constant -- between 0 and 1 Example: F(t-1) = 100; A(t-1) = 110; alpha = 0.4 -- Find F(t) F(t) = 104 Can add parameters for trends and seasonality

11. Trend Projections Use Linear regression Model: yhat = a + b* x a = y-intercept: forecast at period 0 b = slope: rate of change in y for each period x Example: Sales = 100 + 10 * t, where t is period For t = 15, Find yhat -- yhat = 250 Can find and a and b via Method of Least Squares

12. Linear Regression Model: yhat = a + b1 * x1 + b2 * x2 + … + bk * xk a = y-intercept bi = slope: rate of change in y for each increase in xi, given that other xj’s are held constant Example: College GPA = 0.2 + 0.5 HS GPA + 0.001 HS SAT For a HS student with a 3.0 GPA and 1200 SAT - what is the forecast? The forecast college GPA = 2.90 Can find a, b1, and b2 via Method of Least Squares