In-Sample Confidence Bands and Out-of-Sample Forecast Bands for Time-Varying Parameters in Observation Driven Models
Tinbergen Institute Discussion Paper 15-083/III
34 Pages Posted: 11 Jul 2015
Date Written: March 31, 2015
Abstract
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.
Keywords: autoregressive conditional duration, delta-method, generalized autoregressive conditional heteroskedasticity, score driven models, time-varying mean
JEL Classification: C52, C53
Suggested Citation: Suggested Citation