我用卡尔曼滤波估计三因子广义高斯仿射模型(参考文献:范龙振,上交所利率期限结构的三因子广义高斯仿射模型),在eviews中定义状态空间模型如下:
n1=C(1)-(C(51)^2/(C(41)^2*1))*(1-2*(1-EXP(-C(41)*1))/C(41)+(1-EXP(-2*C(41)*1))/(2*C(41)))-(C(52)^2/(C(42)^2*1))*(1- 2*(1-EXP(-C(42)*1))/C(42)+(1-EXP(-2*C(42)*1))/(2*C(42)))-(C(53)^2/(C(43)^2*1))*(1-2*(1-EXP(-C(43)*1))/C(43)+(1- EXP(-2*C(43)*1))/(2*C(43)))+((1-EXP(-C(41)*1))/(C(41)*1))*SV1+((1-EXP(-C(42)*1))/(C(42)*1))*SV2+((1-EXP(- C (43)*1))/(C(43)*1))*SV3+[VAR=C(61)]
n2=C(1)-(C(51)^2/(C(41)^2*2))*(2-2*(1-EXP(-C(41)*2))/C(41)+(1-EXP(-2*C(41)*2))/(2*C(41)))-(C(52)^2/(C(42)^2*2))*(2- 2*(1-EXP(-C(42)*2))/C(42)+(1-EXP(-2*C(42)*2))/(2*C(42)))-(C(53)^2/(C(43)^2*2))*(2-2*(1-EXP(-C(43)*2))/C(43)+(1- EXP(-2*C(43)*2))/(2*C(43)))+((1-EXP(-C(41)*2))/(C(41)*2))*SV1+((1-EXP(-C(42)*2))/(C(42)*2))*SV2+((1-EXP(- C(43)*2))/(C(43)*2))*SV3+[VAR=C(62)]
n3=C(1)-(C(51)^2/(C(41)^2*3))*(3-2*(1-EXP(-C(41)*3))/C(41)+(1-EXP(-2*C(41)*3))/(2*C(41)))-(C(52)^2/(C(42)^2*3))*(3- 2*(1-EXP(-C(42)*3))/C(42)+(1-EXP(-2*C(42)*3))/(2*C(42)))-(C(53)^2/(C(43)^2*3))*(3-2*(1-EXP(-C(43)*3))/C(43)+(1- EXP(-2*C(43)*3))/(2*C(43)))+((1-EXP(-C(41)*3))/(C(41)*3))*SV1+((1-EXP(-C(42)*3))/(C(42)*3))*SV2+((1-EXP(- C(43)*3))/(C(43)*3))*SV3+[VAR=C(63)]
n4=C(1)-(C(51)^2/(C(41)^2*4))*(4-2*(1-EXP(-C(41)*4))/C(41)+(1-EXP(-2*C(41)*4))/(2*C(41)))-(C(52)^2/(C(42)^2*4))*(4- 2*(1-EXP(-C(42)*4))/C(42)+(1-EXP(-2*C(42)*4))/(2*C(42)))-(C(53)^2/(C(43)^2*4))*(4-2*(1-EXP(-C(43)*4))/C(43)+(1- EXP(-2*C(43)*4))/(2*C(43)))+((1-EXP(-C(41)*4))/(C(41)*4))*SV1+((1-EXP(-C(42)*4))/(C(42)*4))*SV2+((1-EXP(- C(43)*4))/(C(43)*4))*SV3+[VAR=C(64)]
n5=C(1)-(C(51)^2/(C(41)^2*5))*(5-2*(1-EXP(-C(41)*5))/C(41)+(1-EXP(-2*C(41)*5))/(2*C(41)))-(C(52)^2/(C(42)^2*5))*(5- 2*(1-EXP(-C(42)*5))/C(42)+(1-EXP(-2*C(42)*5))/(2*C(42)))-(C(53)^2/(C(43)^2*5))*(5-2*(1-EXP(-C(43)*5))/C(43)+(1- EXP(-2*C(43)*5))/(2*C(43)))+((1-EXP(-C(41)*5))/(C(41)*5))*SV1+((1-EXP(-C(42)*5))/(C(42)*5))*SV2+((1-EXP(- C(43)*5))/(C(43)*5))*SV3+[VAR=C(65)]
@STATE SV1=EXP(-(C(41)-C(11)))*SV1(-1)+C(10)/(C(41)-C(11))-C(10)*EXP(-(C(41)-C(11)))/(C(41)-C(11))+[VAR=C(51)^2*(1-EXP(-2*(C(41)-C(11))))/(2*(C(41)-C(11)))]
@STATE SV2=EXP(-(C(42)-C(22)))*SV2(-1)+C(20)/(C(42)-C(22))-C(20)*EXP(-(C(42)-C(22)))/(C(42)-C(22))+[VAR=C(52)^2*(1-EXP(-2*(C(42)-C(22))))/(2*(C(42)-C(22)))]
@STATE SV3=EXP(-(C(43)-C(33)))*SV3(-1)+C(30)/(C(43)-C(33))-C(30)*EXP(-(C(43)-C(33)))/(C(43)-C(33))+[VAR=C(53)^2*(1-EXP(-2*(C(43)-C(33))))/(2*(C(43)-C(33)))]
其中,n1,n2,n3,n4,n5为可观测变量(分别有849个样本量),C(41),C(42),C(43),C(51),C(52),C(53),C(10),C(20),C(30),C(11),C(22),C(33),C(61),C(62),C(63),C(64),C(65) 都为待估计参数。
模型我已经检查好几遍,并没有发现问题,但就是在估计时总是会出现“Missing value found in state innovation vector”提示,不知道这是什么意思?到底是什么地方出了问题?还望各位牛人不吝赐教!
多谢!!!