CBE Forecasting 3 — Questions and Answers
Question 1: When the smoothing parameter α in exponential smoothing is set close to 1, the forecast:
- Heavily weights all past observations equally
- Reacts slowly to recent changes
- Places almost all weight on the most recent observation (Correct answer)
- Is equivalent to a long moving average
Correct answer: Places almost all weight on the most recent observation
An α near 1 means the new forecast is almost entirely the most recent actual value, making the model very responsive to the latest data.
Question 2: Autocorrelation in forecast residuals most directly indicates:
- Heteroskedasticity in the error terms
- The model has not fully captured the data's time-series structure (Correct answer)
- The independent variables are collinear
- Structural breaks in the data
Correct answer: The model has not fully captured the data's time-series structure
Autocorrelated residuals signal that predictable patterns remain unexploited by the model, implying the forecasting specification is incomplete.
Question 3: A leading indicator is best defined as a variable that:
- Moves in tandem with the business cycle
- Changes after the economy has shifted
- Tends to change before the economy as a whole (Correct answer)
- Measures current economic output levels
Correct answer: Tends to change before the economy as a whole
Leading indicators peak and trough before the overall economy, making them useful for anticipating future economic turning points.
Question 4: In an ARIMA(p,d,q) model, the 'd' parameter represents:
- The number of autoregressive terms
- The order of differencing applied to achieve stationarity (Correct answer)
- The number of moving-average terms
- The lag length selected by AIC
Correct answer: The order of differencing applied to achieve stationarity
Differencing (d times) removes unit roots and non-stationarity so that the ARIMA model's AR and MA components can be applied reliably.
Question 5: Forecast bias is present when:
- Error variance increases with the level of the series
- The mean forecast error is consistently positive or negative (Correct answer)
- Residuals exhibit changing variance over time
- The model overfits in-sample data
Correct answer: The mean forecast error is consistently positive or negative
Bias means the forecast systematically over- or under-predicts; an unbiased forecast has errors that average to zero over time.
Question 6: Which scenario calls for multiplicative rather than additive decomposition?
- Seasonal swings are roughly constant in absolute size
- The series has no trend component
- Seasonal variation grows proportionally with the trend level (Correct answer)
- Residuals are normally distributed
Correct answer: Seasonal variation grows proportionally with the trend level
Multiplicative decomposition is appropriate when seasonal fluctuations fan out as the trend level rises, because the seasonal effect scales with the series.
Question 7: The Akaike Information Criterion (AIC) is used in forecasting primarily to:
- Test for unit roots in a time series
- Compare models by balancing fit and parsimony (Correct answer)
- Measure the mean absolute forecast error
- Assess the normality of residuals
Correct answer: Compare models by balancing fit and parsimony
AIC penalizes model complexity, rewarding good fit while discouraging over-parameterization, making it a standard tool for model selection.
CBE Forecasting 3
When the smoothing parameter α in exponential smoothing is set close to 1, the forecast: