You have an ARMA(3,2) model of some financial market data that you estimated using least squares and which you have been using to forecast for several years. The data exhibit time-varying volatility. Which of the following is true?

Question

BlackTom AI · Accepted Answer

Consider the scenario: an ARMA(3,2) model estimated by least squares is being used for forecasting, and the data exhibit time-varying volatility. This suggests heteroskedasticity in the residuals, which standard ARMA models do not capture. Now evaluate each option in turn.
Option 1: 'You can improve the accuracy of your point forecasts using a GARCH model.' Point forecasts are the expected values of the time series. GARCH models are designed to describe and forecast conditional variances, not the conditional mean. Therefore, adding a GARCH component does not necessarily improve point forecasts, and this statement is generally incorrect.
Option 2: 'You can improve the accuracy of your point and interval forecasts using a GARCH model.' While a GARCH model can improve variance estimates, it does not directly improve the point forecast of the mean unless the mean dynamics are also misspecified. Since the question focuses on volatility clustering, the claim that both point and interval forecasts improve is too strong and often inaccurate in isolation.
Option 3: 'You can improve the accuracy of your interval forecasts using a GARCH model.' This is the commonly cited benefit: GARCH captures changing volatility (conditional heteroskedasticity), leading to more accurate prediction intervals that reflect the current volatility regime. Interval forecasts depend on the distribution of future shocks and their variance; modeling that variance with GARCH improves the realism of those intervals.
Option 4: 'You can improve the accuracy of neither your point nor your interval forecasts using a GARCH model.' Given the presence of time-varying volatility, ignoring it typically leads to under- or over- confident intervals. Therefore, this blanket negation is overly pessimistic and ignores the established benefit of GARCH for interval estimation.
In summary, the key insight is that GARCH targets conditional volatility and primarily enhances the reliability of interval forecasts by better matching the time-varying uncertainty, rather than the unconditional point forecasts of the mean. The option that aligns with this understanding is the one about interval forecasts.

You have an ARMA(3,2) model of some financial market data that you estimated using least squares and which you have been using to forecast for several years. The data exhibit time-varying volatility. Which of the following is true?

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