Time-Varying Risk Attitude and Conditional Skewness

Table 3

Model estimation results.

(a)

Parameter		S&P 500	Dow J.	Nasdaq	NYSE	N 225	FTSE 100	SSE
Time- varying 𝛾	𝜌0	0.014061; (0.0668)	0.024333; (0.0960)	0.073175; (0.0220)	0.015498; (0.1171)	0.004656; (0.3741)	0.022537; (0.0356)	0.060807; (0.0767)
	𝜌1	0.671156; (0.0000)	0.548122; (0.0059)	−0.672522; (0.0011)	0.699180; (0.0000)	0.864550; (0.0000)	0.552242; (0.0000)	−0.802902; (0.0013)
	𝜌2	−0.070729; (0.0002)	−0.056227; (0.0098)	0.034182; (0.0169)	−0.045118; (0.0142)	−0.017348; (0.1723)	−0.082743; (0.0000)	0.018254; (0.2415)
Variance equation	𝛼0	0.011472; (0.0000)	0.011674; (0.0000)	0.010696; (0.0000)	0.014906; (0.0000)	0.020784; (0.0038)	0.010016; (0.0002)	0.041504; (0.0000)
	𝛼1	0.075448; (0.0000)	0.081726; (0.0000)	0.046647; (0.0000)	0.078346; (0.0000)	0.092420; (0.0000)	0.096733; (0.0000)	0.099855; (0.0000)
	𝛼2	0.913434; (0.0000)	0.908752; (0.0000)	0.945602; (0.0000)	0.906232; (0.0000)	0.900605; (0.0000)	0.894667; (0.0000)	0.893033; (0.0000)
Skewness equation	𝛽0	−0.000538; (0.0046)	−0.001420; (0.0311)	−0.045664; (0.0017)	−0.000449; (0.0010)	−0.046385; (0.0385)	−0.008635; (0.1683)	0.020711; (0.0143)
	𝛽1	0.001963; (0.0235)	0.004560; (0.0516)	0.032296; (0.0000)	0.003019; (0.0067)	0.028283; (0.0016)	0.011915; (0.0359)	0.006473; (0.0442)
	𝛽2	0.987139; (0.0000)	0.959255; (0.0000)	0.533682; (0.0000)	0.983791; (0.0000)	0.595621; (0.0000)	0.843206; (0.0000)	0.626719; (0.0003)
Log likelihood		−1243.670	−1154.630	−1926.634	−1172.428	−1845.429	−1203.899	−2086.479

(b)

Parameter		DAX	CAC 40	GSPTSE	MIBTEL	IGBM	BVSP	Hangseng
Time- varying 𝛾	𝜌0	0.013762; (0.1821)	0.012604; (0.0681)	0.012297; (0.2773)	0.035950; (0.2338)	0.021461; (0.5686)	0.014801; (0.1713)	0.007973; (0.7020)
	𝜌1	0.771009; (0.0000)	0.744133; (0.0000)	0.754400; (0.0002)	0.082012; (0.8789)	0.761071; (0.0623)	0.728769; (0.0000)	0.843089; (0.0367)
	𝜌2	−0.031714; (0.0562)	−0.053187; (0.0023)	−0.024171; (0.1279)	−0.036640; (0.0961)	−0.013422; (0.4694)	−0.032091; (0.0483)	−0.007450; (0.6257)
Variance equation	𝛼0	0.016197; (0.0002)	0.014882; (0.0001)	0.008462; (0.0000)	0.009467; (0.0000)	0.017090; (0.0000)	0.099432; (0.0000)	0.015302; (0.0003)
	𝛼1	0.089870; (0.0000)	0.080974; (0.0000)	0.072330; (0.0000)	0.097325; (0.0000)	0.089791; (0.0000)	0.072369; (0.0000)	0.067647; (0.0000)
	𝛼2	0.902930; (0.0000)	0.909675; (0.0000)	0.918544; (0.0000)	0.895624; (0.0000)	0.897541; (0.0000)	0.894363; (0.0000)	0.925600; (0.0000)
Skewness equation	𝛽0	−0.044249; (0.3287)	−0.012939; (0.0441)	−0.001743; (0.0042)	−0.008658; (0.1932)	−0.008764; (0.2645)	−0.080287; (0.0413)	−0.003197; (0.5593)
	𝛽1	0.013195; (0.2559)	0.018179; (0.0018)	0.006174; (0.0001)	0.007836; (0.0224)	0.010878; (0.1647)	0.008073; (0.0333)	0.001812; (0.4276)
	𝛽2	0.636849; (0.0780)	0.852436; (0.0000)	0.964743; (0.0000)	0.880261; (0.0000)	0.750425; (0.0005)	0.909746; (0.0000)	0.945101; (0.0000)
Log likelihood		−1815.479	−1665.186	−1046.193	−1071.693	−1130.580	−2450.400	−1753.907