Forecasting Approaches to Forecasting:

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Presentation transcript:

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

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)

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

Exponential Smoothing Weighted Moving Average MAt = .50•Xt + .33•Xt-1 + .17•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-1 .005 ≤ α ≤ .30 Forecast F*t+1 = Ft α n .01 199 .05 39 .10 19 .20 9 .30 6

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=5 t t-1 t-2 t-3 t-4 t-5 t-6 t-7 t-8 MAt .20 .20 .20 .20 .20 0 0 0 0 Ft .33 .22 .15 .10 .07 .04 .03 .02 .01 α=.33

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

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

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

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)