Relating stochastic volatility estimation methods

Question

1. What contributions have the authors mentioned in the paper "Relating stochastic volatility estimation methods" ?

2. How many iterations are used to obtain the parameters of the SV model?

3. What is the way to change the location of the knots?

4. How can the authors improve the distance between the observations?

Accepted Answer

While variants of the GARCH model are applied in scores of articles, use of the stochastic volatility model is less widespread.. In this article it is argued that one reason for this difference is the relative difficulty of estimating the unobserved stochastic volatility, and the varying approaches that have been taken for such estimation.. In order to simplify the comprehension of these estimation methods, the main methods for estimating stochastic volatility are discussed, with focus on their commonalities.

Accepted Answer

For the Bayesian methods GMS, SSS, MMS a sample of 10,000 draws from the posterior density is collected, after a burn-in sample of 1,000 iterations for obtaining an initial estimate of H while fixing the parameters, followed by a further 1,000 iterations where both H and parameters are sampled, but not stored.

Accepted Answer

As the elements ht close to the knots are tied down more than elements in between two knots, it is advisable to change the location of the knots between iterations.

Accepted Answer

As all dependence through time is taken up by the simulation smoother and incorporated into the sample H(i), optimising the distance between the observation densities can be done at each time t separately from other time-points.

Accepted Answer

If the auxiliary model indeed covers the important characteristics of the data, and if the auxiliary sample size TAux is sufficiently large, then optimising Q(θ; θ̂Aux) provides an efficient estimate of the parameters θ of the SV model (see also Andersen et al., 1999).

Accepted Answer

The sampler can be started using the parameter estimates from the univariate samplers as initial values, initialising the correlation sequence at the fixed fullsample correlation.

Accepted Answer

For GMS, the approximation was far more precise using a mixture of several normal densities, and the problem of the bias was mostly solved for parameter estimation.

Accepted Answer

By iterating back and forth between improving estimates of Y ∗ and extracting a new H̃, an optimal solution for the parameters can be found in what is usually a small number of iterations (Sandmann and Koopman, 1998).

Accepted Answer

the score vector of the auxiliary model should be scaled by the inverse information matrix of the model, minimising effectivelyQ(θ; θ̂Aux) = sAux(Y ∗(θ), θ̂Aux)′I−1(θ̂Aux)sAux(Y ∗(θ), θ̂Aux),I(θ̂Aux) = 1 T ∑ ∂ lnPAux(yt; θAux) ∂θAux ∂ lnPAux(yt; θAux) ∂θ′Aux ⌋ θAux=θ̂Aux .

Accepted Answer

The resulting linear Gaussian state space model is amenable to evaluation using the Kalman filter equations, which deliver the likelihood of this model efficiently.

Accepted Answer

Improving on IS with IISThe IS method of estimating a SV model is flexible, relatively easy to implement, and not too computationally intensive in practice either.

Accepted Answer

This acceptance rate is negatively related with the blocksize, and in this case if the acceptance rate drops below around 0.9, the efficiency of the sampler starts to deteriorate with blocksize.

Accepted Answer

The three aforementioned methods all have their drawbacks: QML is only approximative, GMS does not provide a classical maximum likelihood estimator, and SMM lacks an estimate for the state of the volatility.

Relating stochastic volatility estimation methods

Chat with Paper

AI Agents for this Paper

Most frequently asked questions

1. What contributions have the authors mentioned in the paper "Relating stochastic volatility estimation methods" ?

2. How many iterations are used to obtain the parameters of the SV model?

3. What is the way to change the location of the knots?

4. How can the authors improve the distance between the observations?

5. What is the way to estimate the parameters of the SV model?

6. What is the correlation sequence for the univariate sampler?

7. What was the problem of the bias in the approximation of the QML?

8. How many iterations can be used to improve the estimates of Y?

9. What is the auxiliary model's score vector?

10. What is the simplest way to estimate the likelihood of the Gaussian state space model?

11. What is the way to estimate a SV model?

12. What is the acceptance rate of the Metropolis-Hastings step?

13. What is the main drawback of SMM?

Figures

Citations

Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models

Dealing with Stochastic Volatility in Time Series Using the R Package stochvol

Modeling Univariate and Multivariate Stochastic Volatility in R with stochvol and factorstochvol

COMFORT: A Common Market Factor Non-Gaussian Returns Model

Stochastic volatility forecasting of the Finnish housing market

References

Stochastic volatility : selected readings

Related Papers (5)

Relating Stochastic Volatility Estimation Methods

Bayesian Analysis of Stochastic Volatility Models

Stochastic volatility : likelihood inference and comparison with arch models

Generalized autoregressive conditional heteroskedasticity

Bayesian analysis of stochastic volatility models with fat-tails and correlated errors