# 15-083/III (2015-07-09)

Francisco Blasques, VU University Amsterdam, the Netherlands; Siem Jan Koopman, VU University Amsterdam, the Netherlands; Katarzyna Lasak, VU University Amsterdam, the Netherlands; André Lucas, VU University Amsterdam, the Netherlands
autoregressive conditional duration, delta-method, generalized autoregressive
JEL codes:
C52, C53

We study the performance of alternative methods for calculating in-sample confidence and out of-sample forecast bands for time-varying parameters. The in-sample bands reflect parameter uncertainty only. The out-of-sample bands reflect both parameter uncertainty and innovation uncertainty. The bands are applicable to a large class of observation driven models and 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 the different methods. We illustrate our findings in a volatility analysis for monthly Standard & Poor’s 500 index returns.