1. OUTLINE
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Forecasting

2. General approaches to forecasting
How do you think people predicted events before there were mathematical ways of doing it?
How do you as an individual predict things?

3. What will we cover? Regression - equations Smoothing
MAV (Moving average) with MAD (mean average deviation of the error)
Average with Std dev (include all with prediction of probabilities)
Exponential (select a smoothing constant)
Seasonal (when substantial seasonal variations exist)
Remove the seasonality
Calculate the trend and forecast
Return the seasonality to the trend line

4. Regression equations for confidence and prediction
Confidence Interval for the regression equation at Xo:
± 𝑡 𝛼 2 ,𝑛−2 𝑀𝑆 𝐸 1 𝑛 + 𝑥 0 − 𝑥 𝑆 𝑥𝑥
Prediction for an average of k y values at Xo
± 𝑡 𝛼 2 ,𝑛−2 𝑀𝑆 𝐸 1 𝑘 + 1 𝑛 + 𝑥 0 − 𝑥 𝑆 𝑥𝑥
Prediction for an individual y value at Xo
± 𝑡 𝛼 2 ,𝑛−2 𝑀𝑆 𝐸 𝑛 + 𝑥 0 − 𝑥 𝑆 𝑥𝑥 ,
where 𝑆 𝑥𝑥 = 𝑖=1 𝑛 𝑥 𝑖 − 𝑥 for each of each above

5. MAV – Moving Average
Average the last n periods of demand
Usually n =3 to 4 periods
Used when you don’t want to go too far back in time and you think the last few data points are the most representative

6. MAD
Mean average deviation
Sum of the absolute deviations from the mean
Calculated on the forecast compared to the actual

7. Exponential Smoothing
Use a constant smoothing constant (α), usually between 0.2 and 0.4
Takes all values into account, but gives a higher weight to the more recent values
Forecast = previous forecast (α) + previous actual(1- α)

8. Calculate the trend line and extend for the forecast
Seasonal
Seasonal (when substantial seasonal variations exist) – works best when several years of data are available
Remove the seasonality
Calculate the trend and forecast
Return the seasonality to the trend line
Seasonal factor – ratio of current demand divided by the average for the year (a high demand will have a seasonal factor greater than 1)
Remove seasonality by dividing each demand by its seasonal factor (each demand will move closer to the average)
Calculate the trend line and extend for the forecast
Multiply each demand by its seasonal factor

9. Seasonal Example