Jacquier, Polson, Rossi (1994)

[TomDoan]

These programs do the analysis of a stochastic volatility model from "Bayesian Analysis of Stochastic Volatility Models." Eric Jacquier, Nicholas G. Polson and Peter E. Rossi; Journal of Business and Economic Statistics, 1994, 12(4), pp. 371-89 using two techniques. The first does the authors' original suggestion of a Metropolis procedure for drawing the log h's, but uses a more refined method for doing the draws which is quite a bit more efficient. The second uses the rejection method as proposed in Kim, Shephard and Chib(1998), "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models", Review of Economic Studies, vol 65, pp 361-93, but with a similar refinement which improves their approximation. The second form requires the kscpostdraw.src procedure which is also posted here.

As written, this requires 7.3, although that's only for the DENSITY instructions at the end. With 7.0-7.2, just take out the SMOOTHING option on the DENSITY instructions at the end. By the way, this runs in half the time with 7.3 compared with 7.0 due to the optimizations that we have made.

Estimation of SV models such as this by simulation methods (and also by approximation with state-space models) is covered as part of the ARCH, GARCH, and Volatility E-Course.

jpr_metropolis.rpf

Estimation with Metropolis-Hastings

(4.96 KiB) Downloaded 960 times

jpr_rejection.rpf

Estimation with rejection method

(4.01 KiB) Downloaded 970 times

jpr_weekly.rat

Data file

(102.25 KiB) Downloaded 1282 times

kscpostdraw.src

Procedure for rejection method

(2.51 KiB) Downloaded 1050 times

[vtsa]

Dear Tom,
I would like to estimate stochastic volatility model using the MCMC techniques from Jacquier, Polson and Rossi (1994). The RATS program gives posterior density distributions of alpha, delta and sigma values. I don’t know how to extract the estimated values of these parameters. Please help!

[TomDoan]

I'm not sure what you mean by the "estimated" values. The means? Just take the mean of the series that's being run through the DENSITY function.