CMA Statistical Methods & Forecasting 3 — Questions and Answers
Question 1: Which of the following is the best measure of forecast accuracy that penalizes large errors more heavily?
- Mean Absolute Error (MAE)
- Mean Squared Error (MSE) (Correct answer)
- Mean Absolute Percentage Error (MAPE)
- Tracking signal
Correct answer: Mean Squared Error (MSE)
MSE squares the errors before averaging, giving disproportionately higher weight to large forecast deviations.
Question 2: In multiple regression, the Variance Inflation Factor (VIF) is used to diagnose:
- Autocorrelation
- Heteroscedasticity
- Multicollinearity (Correct answer)
- Model overfitting
Correct answer: Multicollinearity
A VIF above 10 (or 5, depending on convention) suggests problematic multicollinearity between predictor variables.
Question 3: A market analyst applies the Box-Jenkins methodology. The correct sequence of steps is:
- Forecast → Identify → Estimate → Diagnose
- Identify → Estimate → Diagnose → Forecast (Correct answer)
- Estimate → Identify → Forecast → Diagnose
- Diagnose → Estimate → Identify → Forecast
Correct answer: Identify → Estimate → Diagnose → Forecast
The Box-Jenkins ARIMA process follows: model identification, parameter estimation, diagnostic checking, then forecasting.
Question 4: If the autocorrelation function (ACF) of a time series cuts off sharply after lag q while the PACF decays gradually, the series likely follows:
- AR(p)
- MA(q) (Correct answer)
- ARMA(p,q)
- Random walk
Correct answer: MA(q)
An MA(q) process has an ACF that cuts off after q lags and a PACF that tails off gradually.
Question 5: A confidence interval for a forecast that widens as the forecast horizon extends indicates:
- Model misspecification
- Increasing uncertainty further into the future (Correct answer)
- Positive autocorrelation in errors
- Overfitting of the model
Correct answer: Increasing uncertainty further into the future
Forecast uncertainty compounds over time, so prediction intervals naturally widen at longer horizons.
Question 6: A seasonal index of 1.25 for Q4 in a multiplicative decomposition model means:
- Q4 sales are 25% below the trend
- Q4 sales are 25% above the annual average trend (Correct answer)
- Q4 has 25 more sales days than average
- The trend grows 25% in Q4
Correct answer: Q4 sales are 25% above the annual average trend
In a multiplicative model, a seasonal index above 1.0 means that quarter's values are proportionally above the baseline trend.
Question 7: Which test is used to determine whether two population variances are equal?
- t-test
- z-test
- F-test (Correct answer)
- Chi-square test
Correct answer: F-test
The F-test compares the ratio of two sample variances to test equality of population variances.
CMA Statistical Methods & Forecasting 3
Which of the following is the best measure of forecast accuracy that penalizes large errors more heavily?