Activity32

Fitting Comparable ETS Models

Let’s compare some ETS specifications including:

Simple exponential smoothing (no trend/seasonality)
Holt’s linear trend method
Holt-Winters seasonal method

Forecast Evaluation Framework

We’ll evaluate using multiple metrics:

MSE: Mean Squared Error (penalizes large errors)
MAE: Mean Absolute Error (more robust)
MAPE: Mean Absolute Percentage Error (scale-independent)
MASE: Mean Absolute Scaled Error (relative to naive forecast)

Visual Verification

Model Diagnostics

We should also check residuals:

Lab Activities

Fit an ETS(A,A,M) and ARIMA(0,1,1) model, then compare their residuals

Part A: Fit both models and compare their accuracy using MASE and RMSE
Part B: Analyze residual diagnostics to determine which model handles autocorrelation better

Solution

Prompt: “Which model shows better residual properties for supply chain forecasting? Justify using ACF plots and Ljung-Box test statistics.”

Activity 2: Transformation Impact Analysis

Part A: Implement Box-Cox transformation on the Holt-Winters model using \(\lambda = 0.2\) Part B: (Optional) Evaluate if transformation improves forecast interval coverage at 95% level

Solution

Prompt: “Does variance stabilization help maintain prediction interval reliability during demand spikes?

Activity 3: Ensemble Forecasting Strategy

Part A: Create equal-weighted average of ETS and ARIMA forecasts
Part B: Verify if ensemble reduces mean error

Solution

Prompt: “When would an ensemble be particularly valuable for cement production planning? Consider both average and worst-case performance.”