Filtering With Confidence: In-sample Confidence Bands For GARCH Filters

There is vast empirical evidence that for many economic variables conditional variances and covariances change over time. Given the importance of heteroscedasticity in finance and macroeconomics1 it is not surprising that estimation of the time-varying volatility has attracted substantial attention in the literature. As any time-varying parameter, volatility can be modelled both with observationand parameter-driven models.2 The observation-driven approach is most notably represented by the family of generalised autoregressive conditional heteroscedastic (GARCH) models originated by Engle (1982) and Bollerslev (1986). Stochastic volatility models are a typical example of the parameter-driven class.3 Additionally, volatility is also estimated with realised measures which are model-free and specific to the literature on heteroscedasticity.4 Of