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Table 4 Estimation for heavy-tailed jump-robust HAR–GARCH(1,1)-NORMAL

From: Heterogeneous autoregressive model with structural break using nearest neighbor truncation volatility estimators for DAX

Estimation

LogRV

LogminRV

LogmedRV

θ C1

−0.573789*

(0.197060)

−0.572602*

(0.175907)

−0.621407*

(0.176719)

Heterogeneous component: θ d1,day

0.238119*

(0.040082)

0.397943*

(0.037278)

0.434135*

(0.037851)

 θ d2,day

0.149237*

(0.041986)

0.075528**

(0.042429)

 

 θ w1,week

0.392877*

(0.078684)

0.302916*

(0.071121)

0.347932*

(0.055810)

 θ m1,month

0.153743*

(0.047953)

0.161430*

(0.043576)

0.149333*

(0.042079)

Break effect for

 θ break, C1

−1.488235*

(0.536629)

−1.249370**

(0.642890)

−1.175957*

(0.606153)

 θ break−d1,day

−0.087813

(0.068330)

−0.189498*

(0.070081)

−0.195154**

(0.066462)

 θ break−d2,day

−0.077450

(0.070632)

0.035078

(0.082032)

 

 θ break−w1,week

−0.151890

(0.147371)

−0.018500

(0.164841)

0.053065

(0.119166)

 θ break−m1,month

0.170241

(0.111817)

0.058175

(0.119320)

0.035186

(0.109871)

GARCH component:

   

 α 0

0.010233*

(0.003360)

0.020017*

(0.008815)

0.010039*

(0.004323)

 ARCH effect, α 1

0.040633*

(0.009244)

0.048335*

(0.013916)

0.043843*

(0.010526)

 GARCH effect, β 1

0.928107*

(0.015973)

0.874404*

(0.043618)

0.915048*

(0.024605)

Selection

 AIC

1.674161

1.478626

1.404343

 SIC

1.719692

1.524157

1.442849

 HIC

1.691111

1.495576

1.418677

Diagnostic

 Q(10) for standardized a t

7.9452

7.4558

14.238

 Q(10) for standardized a 2 t

7.5748

6.2532

4.5178

  1. *, ** indicate 5 and 10 % level of significance respectively