CMA Statistical Methods & Forecasting 2 — Questions and Answers
Question 1: In a time series decomposition, which component captures repeating patterns tied to calendar periods shorter than one year?
- Trend
- Cyclical
- Seasonal (Correct answer)
- Irregular
Correct answer: Seasonal
Seasonal components reflect regular fluctuations that repeat within a year, such as holiday sales spikes or summer demand peaks.
Question 2: A market analyst runs a regression of sales (Y) on advertising spend (X) and obtains R² = 0.81. What does this mean?
- Advertising causes 81% of sales
- 81% of sales variation is explained by advertising spend (Correct answer)
- The model has 81% accuracy on test data
- There is a 0.81 correlation between residuals and fitted values
Correct answer: 81% of sales variation is explained by advertising spend
R² measures the proportion of variance in the dependent variable explained by the independent variable(s) in the model.
Question 3: Which smoothing technique assigns exponentially decreasing weights to older observations when forecasting?
- Simple moving average
- Weighted moving average
- Exponential smoothing (Correct answer)
- Hodrick-Prescott filter
Correct answer: Exponential smoothing
Exponential smoothing applies geometrically declining weights so recent data has greater influence on the forecast.
Question 4: A p-value of 0.03 on a regression coefficient means:
- There is a 3% chance the null hypothesis is true
- The coefficient is practically significant
- We reject H₀ at the 5% significance level (Correct answer)
- The model explains 3% of variance
Correct answer: We reject H₀ at the 5% significance level
A p-value below the chosen significance level (0.05) means we reject the null hypothesis that the coefficient equals zero.
Question 5: The Durbin-Watson statistic is primarily used to detect:
- Heteroscedasticity in residuals
- Multicollinearity among predictors
- Autocorrelation in regression residuals (Correct answer)
- Non-normality of the dependent variable
Correct answer: Autocorrelation in regression residuals
The Durbin-Watson statistic tests for first-order serial correlation in the residuals of a regression model.
Question 6: A forecaster uses a 3-period moving average. The last three sales values are 100, 120, and 110. What is the forecast for the next period?
- 110 (Correct answer)
- 115
- 108
- 120
Correct answer: 110
The 3-period moving average forecast is (100 + 120 + 110) / 3 = 110.
Question 7: In hypothesis testing, a Type II error occurs when:
- A true null hypothesis is rejected
- A false null hypothesis is not rejected (Correct answer)
- The significance level is set too low
- The sample size is too large
Correct answer: A false null hypothesis is not rejected
A Type II error (beta error) means failing to reject H₀ when it is actually false — a missed detection.
CMA Statistical Methods & Forecasting 2
In a time series decomposition, which component captures repeating patterns tied to calendar periods shorter than one year?