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

Table 4

OLE of up-down duration equation.

		Panel A: Up duration equation (𝐷^+𝑘)
Index	𝜋^𝑑+0	𝜋^𝑑+1,1	𝜋^𝑑+2,1	𝜎𝑑^+	𝑅^2	𝐹-stat.	𝑃 value
DJI	3.029***	0.011	0.002	0.511	0.0001	0.021	0.979
	(12.058)	(0.203)	(0.034)
STI	3.080***	−0.021	0.0007	0.514	0.0001	0.025	0.975
	(6.466)	(−0.220)	(0.006)
		Panel B: Down duration equation (𝐷^−𝑘)
Index	𝜋^𝑑−0	𝜋^𝑑−1,1	𝜋^𝑑−2,1	𝜎𝑑^−	𝑅^2	𝐹-stat.	𝑃 value
DJI	2.824***	−0.023	0.085**	0.536	0.023	3.620	0.028
	(16.194)	(−0.562)	(2.107)
STI	3.988***	−0.158	−0.130	0.593	0.035	1.485	0.233
	(7.739)	(−1.241)	(−1.201)
		Panel C: Duration equation (𝐻^20)
Index	𝜋^𝑑0	𝜋^𝑑1,1	𝜋^𝑑2,1	𝜎𝑑	𝑅^2	𝐹-stat.	𝑃 value
DJI	2.924***	−0.023	0.085**	0.116	0.008	2.413	0.090
	(16.194)	(−0.562)	(2.107)
STI	3.555***	−0.090	−0.071	0.553	0.012	1.041	0.355
	(10.240)	(−1.181)	(−0.924)
		Panel D: Asymmetry test
	𝜒^2-stat.	d.f.	𝑃 value
DJI	8.967	4	0.062
STI	4.340	4	0.362

Note: Asterisks ***, **, * indicate significance at the 1%, 5%, 10% level, respectively.
𝑡-statistics are given in parentheses beneath the parameter estimates.
Panel A: ln 𝐷⁺_𝑘=𝜋^𝑑+₀+𝜋^𝑑+_1,1ln𝐷⁺_𝑘−1+𝜋^𝑑+_2,1ln𝐷⁻_𝑘+𝜂^𝑑+_𝑘.
Panel B: ln 𝐷⁻_𝑘=𝜋^𝑑−₀+𝜋^𝑑−_1,1ln𝐷⁻_𝑘−1+𝜋^𝑑−_2,1ln𝐷⁺_𝑘+𝜂^𝑑−_𝑘.
Panel C: 𝜋₀^𝑑+=𝜋₀^𝑑−=𝜋^𝑑₀;  𝜋^𝑑+_1,1=𝜋^𝑑−_1,1=𝜋^𝑑_1,1;  𝜋^𝑑+_2,1=𝜋^𝑑−_2,1=𝜋^𝑑_2,1;  𝜎²_𝑑+=𝜎²_𝑑−=𝜎²_𝑑(𝐻²₀).