This discussion paper led to a chapter in: (L. Bauwens, C.M. Hafner & S. Laurent (Eds.)), Relating stochastic volatility estimation methods (pp. 147-174). New York: Wiley.
Estimation of the volatility of time series has taken off since the introduction of the GARCH and stochastic volatility models. 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. In this manner, the advantages of each method are investigated, resulting in a comparison of the methods for their efficiency, difficulty-of-implementation, and precision.