Time Series Analysis ARIMA Models 2 — Questions and Answers
Question 1: Which information criterion is commonly used for ARIMA model selection?
- AIC (Akaike Information Criterion) (Correct answer)
- R-squared
- Mean Absolute Error
- Durbin-Watson statistic
Correct answer: AIC (Akaike Information Criterion)
AIC balances model fit and complexity, penalizing models with more parameters to avoid overfitting.
Question 2: What does a significant Ljung-Box test on ARIMA residuals indicate?
- Residual autocorrelation remains — model is inadequate (Correct answer)
- The model fits perfectly
- Stationarity is confirmed
- Seasonality is absent
Correct answer: Residual autocorrelation remains — model is inadequate
A significant Ljung-Box p-value means residuals are not white noise, suggesting the ARIMA model has not captured all structure.
Question 3: For a SARIMA model ARIMA(1,1,1)(1,1,1)[12], what does the [12] represent?
- Seasonal period of 12 months (Correct answer)
- 12 AR lags
- 12 MA lags
- 12 differencing steps
Correct answer: Seasonal period of 12 months
The [12] denotes the seasonal period, meaning the seasonal pattern repeats every 12 time steps (monthly data with annual seasonality).
Question 4: What condition must be satisfied for an AR(p) model to be stationary?
- All roots of the characteristic polynomial must lie outside the unit circle (Correct answer)
- All roots must lie inside the unit circle
- The mean must equal zero
- Variance must be zero
Correct answer: All roots of the characteristic polynomial must lie outside the unit circle
Stationarity of an AR model requires that characteristic polynomial roots have modulus greater than 1 (outside the unit circle).
Question 5: Which function in Python's statsmodels library is commonly used to fit ARIMA models?
- ARIMA() (Correct answer)
- arima_fit()
- fit_arima()
- time_series_arima()
Correct answer: ARIMA()
The statsmodels ARIMA() class provides a full interface for specifying and fitting ARIMA models to time series data.
Question 6: What is the Box-Jenkins methodology primarily used for?
- Systematic identification, estimation, and diagnostic checking of ARIMA models (Correct answer)
- Only visualizing time series data
- Computing seasonal indices
- Calculating moving averages
Correct answer: Systematic identification, estimation, and diagnostic checking of ARIMA models
Box-Jenkins is a three-step iterative process: identify model orders, estimate parameters, then check residual diagnostics.
Time Series Analysis ARIMA Models 2
Which information criterion is commonly used for ARIMA model selection?