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Table 3 The simulation results for sequence II \((\epsilon , \sigma _{1}, \sigma _{2})=(0.75, 1, \sqrt{7})\)

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)

0.9680 (0.3430)

0.9390 (0.7960)

0.9400 (0.8040)

(0.1,0.1,3,0.3,0.3)

0.9780 (0.3620)

0.9250 (0.7850)

0.9330 (0.7900)

(0.1,0.1,5,0.5,0.5)

0.9730 (0.3750)

0.9320 (0.8040)

0.9510 (0.7970)

(0.1,0.1,7,0.7,0.7)

0.9680 (0.3750)

0.9380 (0.7980)

0.9410 (0.7850)

(−0.1,−0.1,1,0.1,0.1)

0.9690 (0.3640)

0.9380 (0.7750)

0.9340 (0.8000)

(−0.1,−0.1,3,0.3,0.3)

0.9800 (0.3580)

0.9310 (0.7910)

0.9280 (0.7820)

(−0.1,−0.1,5,0.5,0.5)

0.9690 (0.3480)

0.9240 (0.8050)

0.9350 (0.7860)

(−0.1,−0.1,7,0.7,0.7)

0.9740 (0.3400)

0.9420 (0.7770)

0.9370 (0.7880)

(0.2,0.2,1,0.1,0.1)

0.9700 (0.3940)

0.9310 (0.7890)

0.9400 (0.7970)

(0.2,0.2,3,0.3,0.3)

0.9740 (0.3700)

0.9360 (0.7960)

0.9330 (0.7800)

(0.2,0.2,5,0.5,0.5)

0.9710 (0.3890)

0.9370 (0.7820)

0.9460 (0.7870)

(−0.2,−0.2,1,0.1,0.1)

0.9700 (0.3890)

0.9370 (0.7820)

0.9230 (0.7760)

(−0.2,−0.2,3,0.3,0.3)

0.9630 (0.3940)

0.9420 (0.8110)

0.9380 (0.7840)

(−0.2,−0.2,5,0.5,0.5)

0.9650 (0.3780)

0.9270 (0.7810)

0.9280 (0.7740)

(0.3,0.3,1,0.1,0.1)

0.9660 (0.4020)

0.9190 (0.7720)

0.9470 (0.8060)

(0.3,0.3,3,0.3,0.3)

0.9680 (0.3680)

0.9330 (0.7940)

0.9450 (0.8080)

(−0.3,−0.3,1,0.1,0.1)

0.9710 (0.4050)

0.9270 (0.7720)

0.9350 (0.7900)

(−0.3,−0.3,3,0.3,0.3)

0.9820 (0.3950)

0.9440 (0.7900)

0.9350 (0.7850)

(0.4,0.4,1,0.1,0.1)

0.9670 (0.3610)

0.9420 (0.7940)

0.9420 (0.7750)

(0.4,0.4,1,0.3,0.3)

0.9690 (0.3740)

0.9360 (0.7960)

0.9470 (0.8010)

(−0.4,−0.4,1,0.1,0.1)

0.9740 (0.4120)

0.9250 (0.7790)

0.9330 (0.7930)

(−0.4,−0.4,1,0.3,0.3)

0.9760 (0.3970)

0.9440 (0.8030)

0.9260 (0.7890)

(0.5,0.5,1,0.1,0.1)

0.9800 (0.4140)

0.9310 (0.8010)

0.9320 (0.7960)

(−0.5,−0.5,1,0.1,0.1)

0.9820 (0.4290)

0.9370 (0.7910)

0.9390 (0.7930)