Modeling Energy Price Dynamics: GARCH versus Stochastic Volatility

Joshua Chan and Angelia Grant (2016)
Energy Economics, 54, 182-189
[ Journal Version | Working Paper | Code ]

This code estimates seven stochastic volatility and seven GARCH models. It also computes density forecasts from these models. The application is illustrated using nine series of oil, petroleum product and natural gas prices.

This code also computes the marginal likelihood for each model using the improved cross-entropy method developed in Chan and Eisenstat (2015).

The seven stochastic volatility models are:

1. SV: stochastic volatility model where the log volatility follows a stationary AR(1)
2. SV-2: same as SV but the log volatility follows a stationary AR(2)
3. SV-J: same as SV but the prices equation has a "jump" component
4. SV-M: same as SV but the log volatility enters the prices equation as a covariate
5. SV-MA:same as SV but the observation error follows an MA(1)
6. SV-t: same as SV but the observation error follows a Student's t distribution
7. SV-L: SV with a leverage effect

The seven GARCH models are:

1. GARCH: GARCH(1,1) model where the variance process follows a stationary AR(1)
2. GARCH-2: same as GARCH but the variance process follows a stationary AR(2)
3. GARCH-J: same as GARCH but the prices equation has a "jump" component
4. GARCH-M: same as GARCH but the variance enters the prices equation as a covariate
5. GARCH-MA:same as GARCH but the observation error follows an MA(1)
6. GARCH-t: same as GARCH but the observation error follows a Student's t distribution
7. GARCH-GJR: GARCH with a leverage effect