Time Series Analysis ARIMA Models 2

Question 1

Which information criterion is commonly used for ARIMA model selection?

Accepted Answer

AIC (Akaike Information Criterion)

Answer

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?

Accepted Answer

Residual autocorrelation remains — model is inadequate

Answer

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?

Accepted Answer

Seasonal period of 12 months

Answer

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?

Accepted Answer

All roots of the characteristic polynomial must lie outside the unit circle

Answer

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?

Accepted Answer

ARIMA()

Answer

The statsmodels ARIMA() class provides a full interface for specifying and fitting ARIMA models to time series data.

Time Series Analysis Practice Test