1. Forecasting Approaches to Forecasting:
A) Judgmental Analysis - Subjective Estimate
B) Causal Models (Econometrics)
Res Units = b0 + b1(Housing Starts) + b2(Savings Inflow)
C) Time Series Models - Use Past Demand Pattern to Predict the Future
1) Moving Average
2) Exponential Smoothing
3) Regression

2. Components of a Demand Pattern:
1) Average Demand - Constant Term
2) Noise - Random Variation
3) Trend - Growth or Decline (linear)
4) Seasonality - Regular Repeating Cycle
Moving Average - Average of past n Demands (6 ≤ n ≤ 200)

3. Example:
Week Xt Mat Forecast Error
1 105
2 130
3 85
4 102
5 110
6 90
7 105
8 95
9 115
10 120
11 80
12 95
13 100

4. Exponential Smoothing
Weighted Moving Average
MAt = .50•Xt + .33•Xt •Xt-2
Exponential Smoothing
New Ave = Old Ave + Correction
Ft - Ave Demand (Constant Term)
Ft = Ft-1 + α(Xt - Ft-1)
Ft = α•Xt + (1-α)Ft ≤ α ≤ .30
Forecast F*t+1 = Ft
α n
.05 39
.10 19
.20 9
.30 6

5. Weighting of Past Demands n=5 t t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8
Period Xt MAt (n=4) Ft (α=.4)
1 40
2 40
3 40
4 40
5 60
6 60
7 60
8 60
9 60
Weighting of Past Demands
n= t t t t t t t t t-8
MAt Ft
α=.33

6. Example:
Week Xt Ft Forecast Error
1 105
2 130
3 85
4 102
5 110
6 90
7 105
8 95
9 115
10 120
11 80
12 95
13 100

7. Exponential Smoothing with Trend – Holt Model
Smooth Ave Demand
Smooth Ave Trend
Forecast:
t-1 t

8. Exponential Smoothing with Trend & Seasonality – Holt-Winters Model
Seasonal Index = Actual Demand/Ave Demand
Smooth Ave Demand
Smooth Ave Trend
3) Smooth Ave Index
Forecast

9. Durban-Watson Statistic:
If the data is Curvilinear rather than Linear there will be a high
level of Auto-Correlation between the neighboring residuals
Durban-Watson Test:
H0: ρ = 0 No Auto-Correlation
HA: ρ > 0 Positive Auto-Correlation
Ac: d > du
Re: d < dl
(n ≥ 15)