To jump or not to jump: momentum of jumps in crude oil price volatility prediction

Financial Innovation

Table 1 Full-sample estimation results of the HAR-RV and HAR-CJ models

Variables	h = 1	h = 5	h = 10	h = 22
Panel A: HAR-RV
φ₀	0.199***	0.258***	0.314***	0.410***
	(2.803)	(2.804)	(2.836)	(3.491)
φ_d	0.056	0.067**	0.042*	0.041**
	(1.120)	(2.073)	(1.925)	(2.151)
φ_w	0.356***	0.264**	0.225*	0.210*
	(3.123)	(2.303)	(1.673)	(1.763)
φ_m	0.465***	0.510***	0.540***	0.499***
	(4.383)	(4.227)	(3.683)	(3.327)
R²	0.314	0.544	0.580	0.581
Panel B: HAR-CJ
φ₀	0.264***	0.316***	0.360***	0.439***
	(4.639)	(4.358)	(3.933)	(3.735)
φ_cd	0.116	0.133**	0.095**	0.102***
	(1.609)	(2.449)	(2.458)	(3.258)
φ_cw	0.589***	0.505***	0.481***	0.386***
	(3.773)	(3.869)	(3.595)	(3.213)
φ_cm	0.256**	0.282**	0.300**	0.309**
	(2.213)	(2.277)	(2.082)	(1.979)
φ_sd	0.007	0.013	− 0.003	− 0.007
	(0.186)	(0.571)	(− 0.227)	(− 0.675)
φ_sw	− 0.001	− 0.109	− 0.159**	− 0.073
	(− 0.010)	(− 1.262)	(− 2.098)	(− 0.934)
φ_sm	0.227	0.342*	0.467*	0.493*
	(1.447)	(1.763)	(1.814)	(1.755)
R²	0.342	0.600	0.639	0.622

This table provides the full-sample estimation results of the HAR-RV and HAR-CJ models in Panels A and B, respectively. The HAR-RV model is given by
\(RV_{t + 1:t + h} = \varphi_{0} + \varphi_{d} RV_{t} + \varphi_{w} RV_{t - 4:t} + \varphi_{m} RV_{t - 21:t} + \omega_{t + 1:t + h}\),
where RV is the realized variance, \(RV_{{t + {1}:t + h}} = ({1 \mathord{\left/ {\vphantom {1 h}} \right. \kern-\nulldelimiterspace} h})(RV_{t + 1} + \cdots + RV_{t + h} )\). In particular, \(RV_{t}\), \(RV_{t - 4:t}\) and \(RV_{t - 21:t}\) denotes the daily, weekly, and monthly RVs, respectively, which are all available up to day t. The HAR-CJ model is expressed as
\(RV_{t + 1:t + h} = \varphi_{0} + \varphi_{cd} C_{t} + \varphi_{cw} C_{t - 4:t} + \varphi_{cm} C_{t - 21:t} + \varphi_{sd} SJ_{t} + \varphi_{sw} SJ_{t - 4:t} + \varphi_{sm} SJ_{{t - 2{1}:t}} + \omega_{t + 1:t + h} ,\)
where C and SJ denote the continuous component and significant jump measure, respectively. Coefficient estimates are reported and their t-statistics shown in parentheses below are computed based on a Newey-West correction which allows for serial correlation up to order 5 (h = 1), 10 (h = 5), 20 (h = 10), and 44 (h = 22). The R²s are also reported. *** (**) (*) indicates significance at the 1% (5%) (10%) two-tailed level. The sample period runs from January 3, 2012 to May 11, 2018.