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Table 5 The simulation results for sequence III \((\epsilon , \sigma , k)=(0.5, 1, 3)\)

From: Empirical likelihood inference for threshold autoregressive conditional heteroscedasticity model

\((\theta _{1}, \theta _{2}, \alpha _{0}, \alpha _{1}, \alpha _{2})\)

n = 100

n = 300

n = 500

(0.1,0.1,1,0.1,0.1)

0.9650 (0.3300)

0.9410 (0.7330)

0.9510 (0.7660)

(0.1,0.1,3,0.3,0.3)

0.9560 (0.3260)

0.9410 (0.7390)

0.9280 (0.7440)

(0.1,0.1,5,0.5,0.5)

0.9720 (0.3320)

0.9310 (0.7280)

0.9310 (0.7140)

(0.1,0.1,7,0.7,0.7)

0.9560 (0.3050)

0.9490 (0.7280)

0.9210 (0.7130)

(−0.1,−0.1,1,0.1,0.1)

0.9610 (0.3020)

0.9260 (0.7240)

0.9350 (0.7530)

(−0.1,−0.1,3,0.3,0.3)

0.9710 (0.3300)

0.9390 (0.7310)

0.9430 (0.7560)

(−0.1,−0.1,5,0.5,0.5)

0.9540 (0.3220)

0.9350 (0.7230)

0.9410 (0.7460)

(−0.1,−0.1,7,0.7,0.7)

0.9690 (0.3390)

0.9360 (0.7070)

0.9330 (0.7200)

(0.2,0.2,1,0.1,0.1)

0.9530 (0.3210)

0.9460 (0.7350)

0.9240 (0.7140)

(0.2,0.2,3,0.3,0.3)

0.9670 (0.3140)

0.9400 (0.7260)

0.9290 (0.7550)

(0.2,0.2,5,0.5,0.5)

0.9670 (0.3610)

0.9390 (0.7420)

0.9510 (0.7660)

(−0.2,−0.2,1,0.1,0.1)

0.9560 (0.3490)

0.9390 (0.7280)

0.9400 (0.7490)

(−0.2,−0.2,3,0.3,0.3)

0.9660 (0.3570)

0.9360 (0.7090)

0.9350 (0.7180)

(−0.2,−0.2,5,0.5,0.5)

0.9550 (0.3290)

0.9380 (0.7300)

0.9190 (0.7180)

(0.3,0.3,1,0.1,0.1)

0.9640 (0.3400)

0.9380 (0.7320)

0.9330 (0.7460)

(0.3,0.3,3,0.3,0.3)

0.9670 (0.3780)

0.9340 (0.7320)

0.9350 (0.7560)

(−0.3,−0.3,1,0.1,0.1)

0.9640 (0.3600)

0.9400 (0.7470)

0.9500 (0.7450)

(−0.3,−0.3,3,0.3,0.3)

0.9700 (0.3710)

0.9380 (0.5650)

0.9280 (0.7440)

(0.4,0.4,1,0.1,0.1)

0.9420 (0.7570)

0.9150 (0.5650)

0.9290 (0.7640)

(0.4,0.4,1,0.3,0.3)

0.9570 (0.3810)

0.9350 (0.7380)

0.9440 (0.7430)

(−0.4,−0.4,1,0.1,0.1)

0.9610 (0.4130)

0.9540 (0.7430)

0.9360 (0.7470)

(−0.4,−0.4,1,0.3,0.3)

0.9600 (0.3850)

0.9400 (0.7440)

0.9400 (0.7690)

(0.5,0.5,1,0.1,0.1)

0.9540 (0.3940)

0.9320 (0.754)

0.9250 (0.7640)

(−0.5,−0.5,1,0.1,0.1)

0.9590 (0.4230)

0.9450 (0.7550)

0.9500 (0.7760)