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How to Forecast Volatility of the Conditional Variance in the GARCH Model

To forecast the volatility of the conditional variance using a GARCH model in EViews, follow these steps:

Step-by-Step Guide:

  1. Load Your Data:
    • Open EViews and load your time series data.
  2. Specify the GARCH Model:
    • Go to Quick -> Estimate Equation.
    • In the equation specification box, enter the mean equation (e.g., Y = C(1) + C(2)*X + AR(1)).
    • Click on Options and select ARCH under the Method dropdown.
    • Specify the GARCH model by entering the order of GARCH (p, q) terms. For example, a GARCH(1,1) model.
  3. Estimate the Model:
    • Click OK to estimate the model.
    • EViews will provide the estimated coefficients for the mean equation and the GARCH parameters.
  4. View the Conditional Variance:
    • After estimation, go to View -> GARCH Graphs -> Conditional Variance.
    • This plot shows the time-varying conditional variance.
  5. Forecast Volatility:
    • To forecast future volatility, go to Forecast in the toolbar.
    • Enter the forecast period (e.g., next 10 periods).
    • Ensure the GARCH variance option is selected to forecast the conditional variance.
    • Click OK to generate the forecast.
  6. Interpret the Results:
    • EViews will output the forecasted values of the conditional variance.
    • Analyze the forecast to understand the expected volatility over the forecast period.

Detailed Explanation:

  • GARCH Model Specification:
    • A GARCH(p,q) model combines past variances (GARCH terms) and past squared residuals (ARCH terms) to model volatility.
    • Example: GARCH(1,1) includes one lag of the conditional variance and one lag of the squared residual.
  • Conditional Variance:
    • This represents the forecasted volatility. It is time-varying and adapts based on past behavior of the series.

Practical Example:

Suppose you are analyzing the daily returns of a stock:

  1. Load Data:
    • Import the daily returns into EViews.
  2. Specify and Estimate GARCH Model:
    • Use the equation Returns = C(1) + C(2)*AR(1) and select GARCH(1,1).
  3. View Conditional Variance:
    • Examine the conditional variance plot to see how volatility changes over time.
  4. Forecast Volatility:
    • Forecast the next 10 days to see expected future volatility.
  5. Analyze Forecast:
    • The output will show the expected variance for each of the next 10 days, allowing you to assess risk.

By following these steps, you can effectively forecast the volatility of the conditional variance using a GARCH model in EViews. This method provides insights into the expected future volatility based on past data.

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