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62 M. M. NEVES
4. A few simulation results
An extensive simulation study is being carried out by the author and some results will appear in Prata Gomes and Neves (2015a, 2015b). Here some re- marks and overall comments are given. A brief description of what is being done follows.
Simulated samples are generated from a given process, with ✓ known. A simple path of the estimators ⇥bUC and ⇥bGJ is generated. Through the proce- dures briefly described in Section 3.2 the optimal block length is obtained for each sample and block bootstrap estimates, using that optimal block length, are calculated.
1.8 UC 1.6 GJ 1.4
1.2
1 0.8 0.6 0.4 0.2 0
0 100
UC_Bopt=111 GJ_Bopt=60
1.8 UC 1.6 GJ 1.4
1.2
1 0.8 0.6 0.4 0.2 0
UC_Bopt=100 GJ_Bopt=47
200
300 400
1.4
1.2 GJ
1 0.8 0.6 0.4 0.2 0
500
0 100 200
UC_Bopt=6 GJ_Bopt=7
300 400 500
UC
0 100
200
300 400 500
Figure 7. One sample path of the estimators ⇥b U C and ⇥b GJ for a sample of size n = 500 from the ARMAX process and block boot- strap estimates using “optimal” block length for ✓ = 0.1, ✓ = 0.4 and ✓ = 0.8.
