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

Table 5

MLE of trend equation.

		Panel A: up trend equation (𝑟^+𝑡)
Index	𝜑^+0	𝜑^+1	𝜑^+2	𝜎𝜇+	𝑅^2	𝐹-stat.	𝑃 value
DJI	0.0007***	−0.0080	0.671***	0.011	0.018	67.954	<0.001
	(2.956)	(−0.674)	(11.606)
STI	0.0004	0.013	0.893***	0.012	0.040	42.387	<0.001
	(0.097)	(0.574)	(8.840)
		Panel B: down trend equation (𝑟^−𝑡)
Index	𝜑^−0	𝜑^−1	𝜑^−2	𝜎𝜇−	𝑅^2	𝐹-stat.	𝑃 value
DJI	−0.001***	−0.113***	0.538***	0.012	0.0150	64.694	<0.001
	(−3.926)	(−9.761)	(6.605)
STI	−0.002***	0.008	0.227*	0.013	0.0017	1.965	0.140
	(−3.759)	(0.389)	(1.925)
		Panel C: trend equation(𝐻^30)
Index	𝜑0	𝜑1		𝜎𝜇	𝑅^2	𝐹-stat.	𝑃 value
DJI	−1.74𝐸−6	0.0265***		0.012	0.001	11.334	<0.001
	(−0.019)	(3.367)
STI	−1.31𝐸−5	0.124 ***		0.013	0.015	67.537	<0.001
	(−0.067)	(8.218)
		Panel D: nonlinearity Test
	𝜒^2-stat.	d.f.	𝑃 value
DJI	1035.713	5	<0.001
STI	300.714	5	<0.001

Note: Asterisks ***, **, * indicate significance at the 1%, 5%, 10% level, respectively.
𝑡-statistics are given in parentheses beneath the parameter estimates.
Panel A: 𝑟_𝑡=𝜑⁺₀+𝜑⁺₁𝑟_𝑡−1+𝜑⁺₂𝑚⁺_𝑘,𝑡+𝜀⁺_𝑡.
Panel B: 𝑟_𝑡=𝜑⁻₀+𝜑⁻₁𝑟_𝑡−1+𝜑⁻₂𝑚⁻_𝑘,𝑡+𝜀⁻_𝑡.
Panel C: 𝜑⁺₀=𝜑⁻₀=𝜑₀;𝜑⁺₁=𝜑⁻₁=𝜑₁;𝜑⁺₂=𝜑⁻₂=𝜑₂=0;𝜎²_𝜇+=𝜎²_𝜇−=𝜎²_𝜇(𝐻³₀).