Valueat-Risk

τ=0.25
τ=0.75
−1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4
rv t , rv t w , rv t
m
GARCH(1,1)−EDF
GJR−EDF
1.0 1.5 2.0
rv t , rv t w , rv t
m
GARCH(1,1)−EDF
GJR−EDF
−4 −2 0 2 4
r t+1
−4 −2 0 2 4
r t+1
(a)
(b)
τ=0.025
τ=0.975
rv t , rv t w , rv t
m
GARCH(1,1)−EDF
GJR−EDF
rv t , rv t w , rv t
m
GARCH(1,1)−EDF
GJR−EDF
−6 −5 −4 −3 −2
2 3 4 5
−4 −2 0 2 4
−4 −2 0 2 4
r t+1
r t+1
(c)
(d)
Figure 4: Kernel regression estimates of the quantile forecasts q t,1 (τ) (for τ equal to 0.025, 0.25,
0.75, and 0.975) on the return realization, r t+1 , for the GARCH(1,1)-EDF, GJR-EDF, and the
quantile model with X t = [rv t , rv w t , rv m t ].
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