A Trend-Switching Financial Time Series Model with Level-Duration Dependence

Table 3

OLE of high-low level equation.

			Panel A: high level equation (𝐻𝑘)
Index	𝜋^ℎ0	𝜋^ℎ1,1	𝜋^ℎ1,2	𝜋^ℎ2,1	𝜋^ℎ2,2	𝜎ℎ	𝑅^2	𝐹-stat.	𝑃 value
DJI	0.017***	−0.171***	−0.084	−0.236***	0.117**	0.022	0.230	22.868	<0.001
	(6.44)	(−4.838)	(−1.582)	(−6.346)	(2.307)
STI	0.010	−0.137*	−0.032	−0.291***	0.327***	0.029	0.316	9.387	<0.001
	(1.550)	(−1.765)	(−0.321)	(−3.594)	(3.501)
			Panel B: low level equation (𝐿𝑘)
Index	𝜋^𝑙0	𝜋^𝑙1,1	𝜋^𝑙1,2	𝜋^𝑙2,1	𝜋^𝑙2,2	𝜎𝑙	𝑅^2	𝐹-stat.	𝑃 value
DJI	−0.02***	0.039	0.175***	−0.056	0.224***	0.035	0.099	8.400	<0.001
	(−4.816)	(0.436)	(3.026)	(−0.668)	(3.586)
STI	−0.029***	0.350**	0.442***	−0.164	0.030	0.041	0.191	4.728	0.002
	(−3.193)	(2.342)	(3.905)	(−1.139)	(0.251)
			Panel C: level equation(𝐻^10)
Index	𝜋0^ℎ𝑙	𝜋^ℎ𝑙1,1	𝜋^ℎ𝑙1,2	𝜋^ℎ𝑙2,1	𝜋^ℎ𝑙2,2	𝜎ℎ𝑙	𝑅^2	𝐹-stat.	𝑃 value
DJI	−0.001	−0.209***	0.170***	−0.256***	0.244***	0.030	0.560	195.946	<0.001
	(−0.710)	(−5.376)	(4.409)	(−6.658)	(6.272)
STI	−0.0004	−0.100	0.301***	−0.279***	0.186**	0.039	0.538	48.248	<0.001
	(−0.093)	(−1.310)	(4.116)	(−3.824)	(2.467)
			Panel D: asymmetry test
	𝜒^2-stat.	d.f.	𝑃 value
DJI	121.701	6	<0.001
STI	46.604	6	<0.001

Note: Asterisks ***, **, * indicate significance at the 1%, 5%, and 10% level, respectively.
𝑡-statistics are given in parentheses beneath the parameter estimates.
Panel A: 𝐻_𝑘=𝜋^ℎ₀+𝜋^ℎ_1,1𝐻_𝑘−1+𝜋^ℎ_1,2𝐻_𝑘−2+𝜋^ℎ_2,1𝐿_𝑘+𝜋^ℎ_2,2𝐿_𝑘−1+𝜂^ℎ_𝑘.
Panel B: 𝐿_𝑘=𝜋^𝑙₀+𝜋^𝑙_1,1𝐿_𝑘−1+𝜋^𝑙_1,2𝐿_𝑘−2+𝜋^𝑙_2,1𝐻_𝑘−1+𝜋^𝑙_2,2𝐻_𝑘−2+𝜂^𝑙_𝑘.
Panel C: 𝜋^ℎ₀=𝜋^𝑙₀=𝜋₀^ℎ𝑙;𝜋^ℎ_1,𝑖=𝜋^𝑙_1,𝑖=𝜋^ℎ𝑙_1,𝑖,𝑖=1,2;𝜋^ℎ_2,𝑗=𝜋^𝑙_2,𝑗=𝜋^ℎ𝑙_2,𝑗,𝑗=1,2;𝜎²_ℎ=𝜎²_𝑙=𝜎²_ℎ𝑙(𝐻¹₀).