State space model for volatility forecasting

[hasanov]

In Sadorsky (2006), state space model is specified for volatility and a one period ahead forecast constructed from the estimated model.

r^2(t) = c1 z_1(t) + z_2(t) (1)
z_2(t) = var(exp(c2)) (2)
z_1(t) = z_1(t-1) (3)

where r(t) is the petroleum futures price return. This model describes an unobserved term with an AR(1) process. The variables z1 and z2 are the two state variables.

Eq. (1) is the signal equation and Eqs. (2) and (3) are the state equations.

Is there any procedure and/or instruction in RATS to estimate and forecast volatility using the aforementioned specification given in Sadorsky (2006)?

Sadorsky (2006) Modeling and forecasting petroleum futures volatility. Energy Economics 28, 467-488.

[TomDoan]

Isn't that just a fairly standard state-space model (done with DLM)? z1 is the only state, z2 is the measurement error and (1) is the measurement equation. However, a shock is missing in your equation (3) and there is a problem with scale identification between c1 and the variance in the shock for (3)---perhaps the shock in the RW equation (3) was normalized to a unit variance?

[hasanov]

Thanks, that makes sense !!

[TomDoan]

Note, however, that that has similarities to the well-known stochastic volatility model, but doesn't use a log h model, so there could be some odd behavior since there is nothing forcing the variance estimate to be positive. (Variance is the sum of a state variable and a noise variable, neither of them required to be positive). Basically, it's quite a bit simpler than SV, but has potential issues that SV is designed to avoid.