Table 3 Correlation of the estimators...

Table 3

Correlation of the estimators under the simulation

Panel A. Correlation coefficient between True and other estimators
	(k_M,k_i)	Imp	Hist	Conv-Real	Prac-Real	Real
Coskewness	(3,0)	0.982^***	−0.093^***	−0.009	0.261^***	0.334^***
		(0.000)	(0.000)	(0.394)	(0.000)	(0.000)
	(2,1)	0.989^***	−0.089^***	−0.011	0.280^***	0.348^***
		(0.000)	(0.000)	(0.291)	(0.000)	(0.000)
	(1,2)	0.993^***	−0.085^***	−0.014	0.294^***	0.362^***
		(0.000)	(0.000)	(0.173)	(0.000)	(0.000)
	(0,3)	0.991^***	−0.079^***	−0.014	0.312^***	0.384^***
		(0.000)	(0.000)	(0.151)	(0.000)	(0.000)
Cokurtosis	(4,0)	0.941^***	−0.032^***	0.069^***	0.233^***	0.255^***
		(0.000)	(0.001)	(0.000)	(0.000)	(0.000)
	(3,1)	0.943^***	−0.033^***	0.101^***	0.240^***	0.253^***
		(0.000)	(0.001)	(0.000)	(0.000)	(0.000)
	(2,2)	0.945^***	−0.032^***	0.047^***	0.257^***	0.249^***
		(0.000)	(0.001)	(0.000)	(0.000)	(0.000)
	(1,3)	0.947^***	−0.030^***	−0.012	0.279^***	0.242^***
		(0.000)	(0.002)	(0.240)	(0.000)	(0.000)
	(0,4)	0.947^***	−0.031^***	0.054^***	0.307^***	0.242^***
		(0.000)	(0.002)	(0.000)	(0.000)	(0.000)

Panel A. Correlation coefficient between True and other estimators
	(k_M,k_i)	Imp	Hist	Conv-Real	Prac-Real	Real
Coskewness	(3,0)	0.982^***	−0.093^***	−0.009	0.261^***	0.334^***
		(0.000)	(0.000)	(0.394)	(0.000)	(0.000)
	(2,1)	0.989^***	−0.089^***	−0.011	0.280^***	0.348^***
		(0.000)	(0.000)	(0.291)	(0.000)	(0.000)
	(1,2)	0.993^***	−0.085^***	−0.014	0.294^***	0.362^***
		(0.000)	(0.000)	(0.173)	(0.000)	(0.000)
	(0,3)	0.991^***	−0.079^***	−0.014	0.312^***	0.384^***
		(0.000)	(0.000)	(0.151)	(0.000)	(0.000)
Cokurtosis	(4,0)	0.941^***	−0.032^***	0.069^***	0.233^***	0.255^***
		(0.000)	(0.001)	(0.000)	(0.000)	(0.000)
	(3,1)	0.943^***	−0.033^***	0.101^***	0.240^***	0.253^***
		(0.000)	(0.001)	(0.000)	(0.000)	(0.000)
	(2,2)	0.945^***	−0.032^***	0.047^***	0.257^***	0.249^***
		(0.000)	(0.001)	(0.000)	(0.000)	(0.000)
	(1,3)	0.947^***	−0.030^***	−0.012	0.279^***	0.242^***
		(0.000)	(0.002)	(0.240)	(0.000)	(0.000)
	(0,4)	0.947^***	−0.031^***	0.054^***	0.307^***	0.242^***
		(0.000)	(0.002)	(0.000)	(0.000)	(0.000)

Panel B. Correlation coefficient between Real and other estimators
	(k_M,k_i)	Imp	Hist	Conv-Real	Prac-Real
Coskewness	(3,0)	0.342^***	−0.034^***	0.195^***	0.917^***
		(0.000)	(0.001)	(0.000)	(0.000)
	(2,1)	0.355^***	−0.043^***	0.147^***	0.929^***
		(0.000)	(0.000)	(0.000)	(0.000)
	(1,2)	0.367^***	−0.048^***	0.116^***	0.937^***
		(0.000)	(0.000)	(0.000)	(0.000)
	(0,3)	0.384^***	−0.052^***	0.081^***	0.940^***
		(0.000)	(0.000)	(0.000)	(0.000)
Cokurtosis	(4,0)	0.239^***	0.019^*	0.175^***	0.812^***
		(0.000)	(0.052)	(0.000)	(0.000)
	(3,1)	0.241^***	0.016	0.111^***	0.797^***
		(0.000)	(0.100)	(0.000)	(0.000)
	(2,2)	0.240^***	0.014	0.075^***	0.804^***
		(0.000)	(0.170)	(0.000)	(0.000)
	(1,3)	0.235^***	0.012	0.028^***	0.827^***
		(0.000)	(0.244)	(0.004)	(0.000)
	(0,4)	0.234^***	0.01	0.117^***	0.859^***
		(0.000)	(0.297)	(0.000)	(0.000)

Panel B. Correlation coefficient between Real and other estimators
	(k_M,k_i)	Imp	Hist	Conv-Real	Prac-Real
Coskewness	(3,0)	0.342^***	−0.034^***	0.195^***	0.917^***
		(0.000)	(0.001)	(0.000)	(0.000)
	(2,1)	0.355^***	−0.043^***	0.147^***	0.929^***
		(0.000)	(0.000)	(0.000)	(0.000)
	(1,2)	0.367^***	−0.048^***	0.116^***	0.937^***
		(0.000)	(0.000)	(0.000)	(0.000)
	(0,3)	0.384^***	−0.052^***	0.081^***	0.940^***
		(0.000)	(0.000)	(0.000)	(0.000)
Cokurtosis	(4,0)	0.239^***	0.019^*	0.175^***	0.812^***
		(0.000)	(0.052)	(0.000)	(0.000)
	(3,1)	0.241^***	0.016	0.111^***	0.797^***
		(0.000)	(0.100)	(0.000)	(0.000)
	(2,2)	0.240^***	0.014	0.075^***	0.804^***
		(0.000)	(0.170)	(0.000)	(0.000)
	(1,3)	0.235^***	0.012	0.028^***	0.827^***
		(0.000)	(0.244)	(0.004)	(0.000)
	(0,4)	0.234^***	0.01	0.117^***	0.859^***
		(0.000)	(0.297)	(0.000)	(0.000)

Panel C. Average value of the correlation coefficient between True and other estimators
	(k_M,k_i)	Imp	Hist	Conv-Real	Prac-Real	Real
Coskewness	(2,1)	0.982	−0.096	−0.013	0.217	0.286
	(1,2)	0.985	−0.086	−0.018	0.189	0.241
	(0,3)	0.859	−0.070	−0.023	0.251	0.292
Cokurtosis	(3,1)	0.948	−0.033	0.181	0.224	0.221
	(2,2)	0.955	−0.027	0.118	0.244	0.202
	(1,3)	0.963	−0.018	0.01	0.266	0.209
	(0,4)	0.952	−0.010	0.044	0.267	0.250

Panel C. Average value of the correlation coefficient between True and other estimators
	(k_M,k_i)	Imp	Hist	Conv-Real	Prac-Real	Real
Coskewness	(2,1)	0.982	−0.096	−0.013	0.217	0.286
	(1,2)	0.985	−0.086	−0.018	0.189	0.241
	(0,3)	0.859	−0.070	−0.023	0.251	0.292
Cokurtosis	(3,1)	0.948	−0.033	0.181	0.224	0.221
	(2,2)	0.955	−0.027	0.118	0.244	0.202
	(1,3)	0.963	−0.018	0.01	0.266	0.209
	(0,4)	0.952	−0.010	0.044	0.267	0.250

Panel D. Average value of the correlation coefficient between Real and other estimators
	(k_M,k_i)	Imp	Hist	Conv-Real	Prac-Real
Coskewness	(2,1)	0.291	−0.013	0.217	0.903
	(1,2)	0.240	−0.009	0.131	0.940
	(0,3)	0.262	−0.019	0.021	0.956
Cokurtosis	(3,1)	0.204	0.010	0.110	0.831
	(2,2)	0.185	0.007	0.052	0.842
	(1,3)	0.192	0.007	−0.007	0.827
	(0,4)	0.212	0.006	0.038	0.886

Panel D. Average value of the correlation coefficient between Real and other estimators
	(k_M,k_i)	Imp	Hist	Conv-Real	Prac-Real
Coskewness	(2,1)	0.291	−0.013	0.217	0.903
	(1,2)	0.240	−0.009	0.131	0.940
	(0,3)	0.262	−0.019	0.021	0.956
Cokurtosis	(3,1)	0.204	0.010	0.110	0.831
	(2,2)	0.185	0.007	0.052	0.842
	(1,3)	0.192	0.007	−0.007	0.827
	(0,4)	0.212	0.006	0.038	0.886

Note(s): The table reports correlations among the estimators used in Table 2, with p-values reported in parentheses. Panel A reports the correlations between True and the other estimators, and Panel B reports the correlations between Real and the other ex post estimators. Panels C and D show the average values of 29 correlation coefficients that are estimated using simulated prices with 29 different values of the idiosyncratic variation parameter from Panel B of Table 1. In the first row of each panel, k_M and k_i represent the orders of the index and the stock, respectively. ***, **, and * denote significance at the 99%, 95%, and 90% levels, respectively

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