In-Sample Bounds for Time-Varying Parameters of Observation Driven Models

We study the performance of two analytical methods and one simulation method for computing in-sample confidence bounds for time-varying parameters. These in-sample bounds are designed to reflect parameter uncertainty in the associated filter. They are applicable to the complete class of observation driven models and are valid for a wide range of estimation procedures. A Monte Carlo study is conducted for time-varying parameter models such as generalized autoregressive conditional heteroskedasticity and autoregressive conditional duration models. Our results show clear differences between the actual coverage provided by our three methods of computing in-sample bounds. The analytical methods may be less reliable than the simulation method, their coverage performance is sufficiently adequate to provide a reasonable impression of the parameter uncertainty that is embedded in the time-varying parameter path. We illustrate our findings in a volatility analysis for monthly Standard & Poor's 500 index returns.