Answer: It's widely used to check the independence of residuals in time series models.

## Explanation The Ljung-Box Q statistic is indeed widely used to check the independence of residuals in time series models. This is a crucial step in time series analysis as it helps to ensure that the model's residuals, or the differences between the observed and predicted values, are random and not systematically related. ### Why other options are incorrect: - **Option A**: The Ljung-Box Q statistic can be used for detecting autocorrelation in various time series models, not just autoregressive models. It's a general test for autocorrelation. - **Option B**: The Ljung-Box Q statistic is affected by the number of observations. In fact, the test statistic depends on the sample size and the number of lags being tested. - **Option D**: While the Ljung-Box test is often applied to stationary time series, it can also be used with non-stationary data, though interpretation may be more complex. ### Key Points about Ljung-Box Q Statistic: - Tests whether autocorrelations of residuals are significantly different from zero - Helps validate that model residuals are white noise - Commonly used in ARIMA model diagnostics - Provides a formal statistical test for residual autocorrelation

Author: Tanishq Prabhu