RM5, 6&7

Which one of the following four statements on models for estimating volatility is incorrect?

• In the EWMA model, some positive weight is assigned to the long-run average variance rate.

• In the EWMA model, the weights assigned to observations decrease exponentially as the observations become older.

• In the GARCH(1,1) model, a positive weight is estimated for the long-run average variance rate.

• In the GARCH(1,1) model, the weights estimated for observations decrease exponentially as the observations become older.

When using the Historical Distribution Approach to measure VaR, assuming the return distribution is the first step.

• True

• False

Multiple Correct Answers:

Considering ARCH model and GARCH model:

• GARCH models extend ARCH by incorporating lagged values of volatility

• ARCH model captures the mean-reverting behavior of volatility

• ARCH model captures the persistence behavior of volatility

• GARCH Model Collapses to ARCH model if the autoregressive coefficients of lag variances are statistically insignificantly different from zero.

The Null Hypothesis is the parameter is statistically insignificantly different from zero, and your tolerance level is 5%. If the p-value of the t-statistics is 6%, you should:

• Accept the null hypothesis. The parameter is statistically insignificantly different from zero.

• Reject the null hypothesis. The parameter is statistically insignificantly different from zero.

• Accept the null hypothesis. The parameter is statistically significantly different from zero.

• Reject the null hypothesis. The parameter is statistically significantly different from zero.

Compare GJR-GARCH models and GARCH models

• GJR-GARCH models cannot capture the mean-reverting behaviour of volatility

• GARCH models, unlike GJR-GARCH models, do not have an asymmetric term.

• GJR-GARCH outperforms GARCH models.

• GJR-GARCH nests GARCH model.

Likelihood Ratio Test measures the statistical significance of the difference in the values of Maximized Log-Likelihood between two non-nested models

• True

• False

Considering AIC and BIC:

• Both AIC and BIC are useful for comparing non-nested models.

• Lower (Negative) values of the information criteria, a better model to select.

• AIC tends to select a smaller model.

• BIC tends to select a smaller model.