[Forum SIS] Seminario Jean-Marie Dufour - Università di Bergamo

[Annamaria Bianchi]

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*Lunedì 19 Marzo 2018 *
*Università di Bergamo,*
*via dei Caniana 2, Bergamo*
*Aula 15*
*Ore: 15:00 p.m.*
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*"**Simple Estimators and Inference for Higher-order Stochastic Volatility
Models**"*

*Prof. Jean-Marie Dufour(McGill University, Canada)*


*Abstract*:  We propose several estimators for higher-order stochastic
volatility models, denoted by SV(p), where the latent volatility process is
modeled as an AR(p) process. We discuss stationarity, ergodicity and mixing
properties of SV(p) models. Proposed estimators include two simple
estimators and GMM estimators. Several methods have been proposed in the
literature to estimate SV(1) model, and mostly they are costly from the
computational viewpoint, inflexible across models, not easy to implement
and converge very slowly. Compared to these methods, our simple estimators
for SV(p) models are computationally simple and very easy to apply in
practice. Our simple estimators do not require choosing a sampling
algorithm, initial parameters, and an auxiliary model. Using simple
estimators, we develop recursive estimation procedures for SV(p) models. We
derive asymptotic theories for these estimators and show the usefulness of
these estimators in the context of simulation-based inference technique,
i.e., Monte Carlo (MC) tests. By simulation, we compare our proposed
estimators to the popular Bayesian MCMC estimator. The simple ARMA based
estimator, suggested by this study, in most cases outperforms other
estimators in terms of bias and RMSE. For larger samples, it is uniformly
superior to other estimators. Finally, empirical applications related to
SV(p) models and simple ARMA based estimator are presented. First, SV(p)
models fitted with S&P 500 index returns, and we found that these returns
can be better modeled as an SV(p) model. We also implemented MC tests to
construct more reliable inference and found evidence to support the above
result. Second, we conducted out-of-sample forecasting experiments to study
the accuracy of volatility forecasts among SV(p) models, GARCH models and
Heterogenous Autoregressive model of Realized Volatility (HAR-RV) models.
The results suggested that SV(p) models performed better than other
competing volatility models for forecasting daily volatility. This result
is consistent whether high volatility periods (such as Financial Crisis)
are in the in-sample or in the out-of-sample. Our findings highlight the
importance of using higher-order SV models for forecasting volatility.


Cordiali saluti,

Annamaria Bianchi e Giovanni Urga
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