Confidence Region for long memory based on Inverting Bootstrap Tests: an application to Stock Market Indices

Mardi | 2018-06-26
Salle Sully 5 16h – 17h20

Christian DE PERETTI – Carole SIANI

In the context of long memory, the finite-sample distortion of statistic distributions is so large, that bootstrap confidence intervals (percentile and percentile-t) for the long memory parameter do not perform better than the corresponding asymptotic confidence interval. In this paper, we propose confidence intervals based on inverting bootstrap tests for the long memory parameter. Monte Carlo experiments are carried out for assessing the confidence intervals in finite sample for various situations. The results are graphically displayed using coverage plots and coverage-effectiveness curves for confidence regions. We show that classical confidence intervals (asymptotic as well as bootstrap) have very poor performances, whereas confidence intervals based on inverting bootstrap tests have quite satisfactory performance. These intervals are then applied on stock market indices.