Financial Risk Manager Part 1

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