Table 5 Estimation for heavy-tailed jump-robust HAR–GARCH(1,1)-GED

θ _C1

Heterogeneous component: θ _d1,day

0.243567*

(0.037212)

0.389279*

(0.035970)

0.430507*

(0.036053)

 θ _d2,day

0.146830*

(0.039307)

0.070872**

(0.040519)

 θ _w1,week

0.381336*

(0.074549)

0.310885*

(0.068611)

0.347257*

(0.053792)

 θ _m1,month

0.150149*

(0.045796)

0.164232*

(0.042325)

0.150838*

(0.040687)

Break effect for

 θ _break,C1

 θ _{break−d1,day}

 θ _{break−d2,day}

0.065739

(0.079042)

 θ _{break−w1,week}

0.061224

(0.116876)

 θ _{break−m1,month}

0.142415

(0.109048)

0.051767

(0.117073)

0.022046

(0.108647)

GARCH component

 α ₀

0.010233*

(0.004372)

0.019657**

(0.010186)

0.010080**

(0.005338)

 ARCH effect, α ₁

0.038397*

(0.011729)

0.049301*

(0.016547)

0.043678*

(0.013165)

 GARCH effect, β ₁

0.930122*

(0.020874)

0.874745*

(0.050479)

0.914798*

(0.030635)

 Tail index, λ

1.517782*

(0.079217)

1.654018*

(0.082734)

1.604856*

(0.082409)

Selection

 AIC

1.656853

1.470345

1.392122

 SIC

1.705886

1.519378

1.434128

 HIC

1.675107

1.488599

1.407759

Diagnose

 Q(10) for standardized a _t

8.2971

7.7389

14.462

 Q(10) for standardized a ² _t

8.1479

6.4542

4.6093