Sieve Bootstrap-Based Prediction Intervals for Autoregressive Processes with GARCH Innovations

• Activity Number: 32
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Malaka Thilakaratne*+ and Maduka Rupasignhe and V. A. Samaranayake
• Companies: Missouri University of Science & Technology and Ashland University and Missouri University of Science & Technology
• Keywords: Conditional Heteroskedasticity ; Forecast Intervals ; Residual Bootstrap ; ARMA-GARCH Models ; Volatility

Abstract

A sieve bootstrap-based method for obtaining prediction intervals for autoregressive processes with innovations following a GRACH volatility structure is proposed. Re-sampling is done on residuals obtained after a two-stage process which fits an AR model first and GARCH parameters estimated from the residuals of the AR model. Both the orders of the AR and GARCH processes are considered unknown and are estimated using the AIC and AICC criterion, respectively. This is in contrast to an existing method for ARMA-GARCH processes that assumes both the ARMA and GARCH orders. The proposed method produces intervals that are conditional on the observed data and the interval width is allowed to vary with the conditional variance predicted for the forecast period. A Monte-Carlo simulation study shows that the proposed method produces intervals with coverage probabilities reasonably close to the nominal level.