State Space (Nelson Siegel Extended)

[rodneyleshaba]

Hi Everyone,

I have developed a Svensson code for state space modelling?....The results I get when I make Kalman Filter, State Series and Signal Series are a bit confusing and dont look correct. I am jsut wondering if it has something to do with my code or the data itself....

I just wanted to aolso find out if I am correct to take the signal series as the zero coupon yields of the respective data dates? or should I use the sv output plus c(1) and run the data in excel...

Please see code below:
"@signal _1m = sv1 + sv2*((1-exp(-1/c(1)))/(1/c(1))) +sv3*(((1-exp(-1/c(1)))/(1/c(1)) - exp(-1/c(1)))) + sv4*(((1-exp(-1/c(4)))/(1/c(4)) - exp(-1/c(4)))) + [var = exp(c(5))]

@signal _2m = sv1 + sv2*((1-exp(-2/c(1)))/(2/c(1))) +sv3*(((1-exp(-2/c(1)))/(2/c(1)) - exp(-2/c(1))))+ sv4*(((1-exp(-2/c(4)))/(2/c(4)) - exp(-2/c(4))))+ [var = exp(c(6))]

@signal _3m = sv1 + sv2*((1-exp(-3/c(1)))/(3/c(1))) +sv3*(((1-exp(-3/c(1)))/(3/c(1)) - exp(-3/c(1))))+ sv4*(((1-exp(-3/c(4)))/(3/c(4)) - exp(-3/c(4))))+ [var = exp(c(7))]

@signal _6m =sv1 + sv2*((1-exp(-6/c(1)))/(6/c(1))) +sv3*(((1-exp(-6/c(1)))/(6/c(1)) - exp(-6/c(1)))) + sv4*(((1-exp(-6/c(4)))/(6/c(4)) - exp(-6/c(4)))) + [var = exp(c(8))]

@signal _9m = sv1 + sv2*((1-exp(-9/c(1)))/(9/c(1))) +sv3*(((1-exp(-9/c(1)))/(9/c(1)) - exp(-9/c(1)))) + sv4*(((1-exp(-9/c(4)))/(9/c(4)) - exp(-9/c(4))))+ [var = exp(c(9))]

@signal _12m = sv1 + sv2*((1-exp(-12/c(1)))/(12/c(1))) +sv3*(((1-exp(-12/c(1)))/(12/c(1)) - exp(-12/c(1))))+ sv4*(((1-exp(-12/c(4)))/(12/c(4)) - exp(-12/c(4))))+ [var = exp(c(10))]

@signal _15m = sv1 + sv2*((1-exp(-15/c(1)))/(15/c(1))) +sv3*(((1-exp(-15/c(1)))/(15/c(1)) - exp(-15/c(1))))+ sv4*(((1-exp(-15/c(4)))/(15/c(4)) - exp(-15/c(4))))+ [var = exp(c(11))]

@signal _18m = sv1 + sv2*((1-exp(-18/c(1)))/(18/c(1))) +sv3*(((1-exp(-18/c(1)))/(18/c(1)) - exp(-18/c(1))))+ sv4*(((1-exp(-18/c(4)))/(18/c(4)) - exp(-18/c(4))))+ [var = exp(c(12))]

@signal _21m = sv1 + sv2*((1-exp(-21/c(1)))/(21/c(1))) +sv3*(((1-exp(-21/c(1)))/(21/c(1)) - exp(-21/c(1))))+ sv4*(((1-exp(-21/c(4)))/(21/c(4)) - exp(-21/c(4))))+ [var = exp(c(13))]

@signal _24m = sv1 + sv2*((1-exp(-24/c(1)))/(24/c(1))) +sv3*(((1-exp(-24/c(1)))/(24/c(1)) - exp(-12/c(1)))) + sv4*(((1-exp(-24/c(4)))/(24/c(4)) - exp(-12/c(4)))) + [var = exp(c(14))]

@signal _36m = sv1 + sv2*((1-exp(-36/c(1)))/(36/c(1))) +sv3*(((1-exp(-36/c(1)))/(36/c(1)) - exp(-36/c(1))))+ sv4*(((1-exp(-36/c(4)))/(36/c(4)) - exp(-36/c(4))))+ [var = exp(c(15))]

@signal _48m = sv1 + sv2*((1-exp(-48/c(1)))/(48/c(1))) +sv3*(((1-exp(-48/c(1)))/(48/c(1)) - exp(-48/c(1)))) + [var = exp(c(16))]

@signal _60m = sv1 + sv2*((1-exp(-60/c(1)))/(60/c(1))) +sv3*(((1-exp(-60/c(1)))/(60/c(1)) - exp(-60/c(1)))) + sv4*(((1-exp(-60/c(4)))/(60/c(4)) - exp(-60/c(4)))) + [var = exp(c(17))]

@signal _72m = sv1 + sv2*((1-exp(-72/c(1)))/(72/c(1))) +sv3*(((1-exp(-72/c(1)))/(72/c(1)) - exp(-72/c(1)))) + sv4*(((1-exp(-72/c(4)))/(72/c(4)) - exp(-72/c(4)))) + [var = exp(c(18))]

@signal _84m = sv1 + sv2*((1-exp(-84/c(1)))/(84/c(1))) +sv3*(((1-exp(-84/c(1)))/(84/c(1)) - exp(-84/c(1)))) + sv4*(((1-exp(-84/c(4)))/(84/c(4)) - exp(-84/c(4)))) + [var = exp(c(19))]

@signal _96m = sv1 + sv2*((1-exp(-96/c(1)))/(96/c(1))) +sv3*(((1-exp(-96/c(1)))/(96/c(1)) - exp(-96/c(1))))+ sv4*(((1-exp(-96/c(4)))/(96/c(4)) - exp(-96/c(4)))) + [var = exp(c(20))]

@signal _108m = sv1 + sv2*((1-exp(-108/c(1)))/(108/c(1))) +sv3*(((1-exp(-108/c(1)))/(108/c(1)) - exp(-108/c(1)))) + sv4*(((1-exp(-108/c(4)))/(108/c(4)) - exp(-108/c(4))))+ [var = exp(c(21))]

@signal _120m = sv1 + sv2*((1-exp(-120/c(1)))/(120/c(1))) +sv3*(((1-exp(-120/c(1)))/(120/c(1)) - exp(-120/c(1))))+ sv4*(((1-exp(-120/c(4)))/(120/c(4)) - exp(-120/c(4)))) + [var = exp(c(22))]

@signal _132m = sv1 + sv2*((1-exp(-132/c(1)))/(132/c(1))) +sv3*(((1-exp(-132/c(1)))/(132/c(1)) - exp(-132/c(1))))+ sv4*(((1-exp(-132/c(4)))/(132/c(4)) - exp(-132/c(4)))) + [var = exp(c(23))]

@signal _144m = sv1 + sv2*((1-exp(-144/c(1)))/(144/c(1))) +sv3*(((1-exp(-144/c(1)))/(144/c(1)) - exp(-144/c(1))))+ sv4*(((1-exp(-144/c(4)))/(144/c(4)) - exp(-144/c(4)))) + [var = exp(c(24))]

@signal _156m = sv1 + sv2*((1-exp(-156/c(1)))/(156/c(1))) +sv3*(((1-exp(-156/c(1)))/(156/c(1)) - exp(-156/c(1))))+ sv4*(((1-exp(-156/c(4)))/(156/c(4)) - exp(-156/c(4)))) + [var = exp(c(25))]

@signal _168m = sv1 + sv2*((1-exp(-168/c(1)))/(168/c(1))) +sv3*(((1-exp(-168/c(1)))/(168/c(1)) - exp(-168/c(1)))) + sv4*(((1-exp(-168/c(4)))/(168/c(4)) - exp(-168/c(4)))) + [var = exp(c(26))]


@signal _180m = sv1 + sv2*((1-exp(-180/c(1)))/(180/c(1))) +sv3*(((1-exp(-180/c(1)))/(180/c(1)) - exp(-180/c(1)))) + sv4*(((1-exp(-180/c(4)))/(180/c(4)) - exp(-180/c(4)))) +[var = exp(c(27))]

@signal _192m = sv1 + sv2*((1-exp(-192/c(1)))/(192/c(1))) +sv3*(((1-exp(-192/c(1)))/(192/c(1)) - exp(-192/c(1)))) + sv4*(((1-exp(-192/c(4)))/(192/c(4)) - exp(-192/c(4)))) + [var = exp(c(28))]

@signal _204m = sv1 + sv2*((1-exp(-204/c(1)))/(204/c(1))) +sv3*(((1-exp(-204/c(1)))/(204/c(1)) - exp(-204/c(1))))+ sv4*(((1-exp(-204/c(4)))/(204/c(4)) - exp(-204/c(4)))) + [var = exp(c(29))]

@signal _216m = sv1 + sv2*((1-exp(-216/c(1)))/(216/c(1))) +sv3*(((1-exp(-216/c(1)))/(216/c(1)) - exp(-216/c(1))))+ sv4*(((1-exp(-216/c(4)))/(216/c(4)) - exp(-216/c(4)))) + [var = exp(c(30))]

@signal _228m = sv1 + sv2*((1-exp(-228/c(1)))/(228/c(1))) +sv3*(((1-exp(-228/c(1)))/(228/c(1)) - exp(-228/c(1))))+ sv4*(((1-exp(-228/c(4)))/(228/c(4)) - exp(-228/c(4)))) + [var = exp(c(31))]

@signal _240m = sv1 + sv2*((1-exp(-240/c(1)))/(240/c(1))) +sv3*(((1-exp(-240/c(1)))/(240/c(1)) - exp(-240/c(1))))+ sv4*(((1-exp(-240/c(4)))/(240/c(4)) - exp(-240/c(4)))) + [var = exp(c(32))]

@signal _252m = sv1 + sv2*((1-exp(-252/c(1)))/(252/c(1))) +sv3*(((1-exp(-252/c(1)))/(252/c(1)) - exp(-252/c(1)))) + sv4*(((1-exp(-252/c(4)))/(252/c(4)) - exp(-252/c(4))))+ [var = exp(c(33))]

@signal _264m = sv1 + sv2*((1-exp(-264/c(1)))/(264/c(1))) +sv3*(((1-exp(-264/c(1)))/(264/c(1)) - exp(-264/c(1)))) + sv4*(((1-exp(-264/c(4)))/(264/c(4)) - exp(-264/c(4)))) + [var = exp(c(34))]

@signal _276m = sv1 + sv2*((1-exp(-276/c(1)))/(276/c(1))) +sv3*(((1-exp(-276/c(1)))/(276/c(1)) - exp(-276/c(1)))) + sv4*(((1-exp(-276/c(4)))/(276/c(4)) - exp(-276/c(4)))) + [var = exp(c(35))]

@signal _288m = sv1 + sv2*((1-exp(-288/c(1)))/(288/c(1))) +sv3*(((1-exp(-288/c(1)))/(288/c(1)) - exp(-288/c(1)))) + sv4*(((1-exp(-288/c(4)))/(288/c(4)) - exp(-288/c(4)))) + [var = exp(c(36))]

@signal _300m = sv1 + sv2*((1-exp(-300/c(1)))/(300/c(1))) +sv3*(((1-exp(-300/c(1)))/(300/c(1)) - exp(-300/c(1)))) + sv4*(((1-exp(-300/c(4)))/(300/c(4)) - exp(-300/c(4)))) + [var = exp(c(37))]

@signal _312m = sv1 + sv2*((1-exp(-312/c(1)))/(312/c(1))) +sv3*(((1-exp(-312/c(1)))/(312/c(1)) - exp(-312/c(1)))) + sv4*(((1-exp(-312/c(4)))/(312/c(4)) - exp(-312/c(4)))) + [var = exp(c(38))]

@signal _324m = sv1 + sv2*((1-exp(-324/c(1)))/(324/c(1))) +sv3*(((1-exp(-324/c(1)))/(324/c(1)) - exp(-324/c(1)))) + sv4*(((1-exp(-324/c(4)))/(324/c(4)) - exp(-324/c(4)))) + [var = exp(c(39))]

@signal _336m = sv1 + sv2*((1-exp(-336/c(1)))/(336/c(1))) +sv3*(((1-exp(-336/c(1)))/(336/c(1)) - exp(-336/c(1))))+ sv4*(((1-exp(-336/c(4)))/(336/c(4)) - exp(-336/c(4)))) + [var = exp(c(40))]

@signal _348m = sv1 + sv2*((1-exp(-348/c(1)))/(348/c(1))) +sv3*(((1-exp(-348/c(1)))/(348/c(1)) - exp(-348/c(1))))+ sv4*(((1-exp(-348/c(4)))/(348/c(4)) - exp(-348/c(4)))) + [var = exp(c(41))]

@signal _360m = sv1 + sv2*((1-exp(-360/c(1)))/(360/c(1))) +sv3*(((1-exp(-360/c(1)))/(360/c(1)) - exp(-360/c(1)))) + sv4*(((1-exp(-360/c(4)))/(360/c(4)) - exp(-360/c(4)))) + [var = exp(c(42))]

@state sv1 = c(43) + c(44)*sv1(-1) + c(45)*sv2(-1) + c(46)*sv3(-1) +c(47)*sv4(-1) + [ename = e1, var = exp(c(48))]

@state sv2 = c(49) + c(50)*sv1(-1) + c(51)*sv2(-1) + c(52)*sv3(-1) +c(53)*sv4(-1) + [ename = e2, var = exp(c(54))]

@state sv3 = c(55) + c(56)*sv1(-1) + c(57)*sv2(-1) + c(58)*sv3(-1) +c(59)*sv4(-1) + [ename = e3, var = exp(c(60))]

@state sv4 = c(61) + c(62)*sv1(-1) + c(63)*sv2(-1) + c(64)*sv3(-1) +c(65)*sv4(-1) + [ename = e4, var = exp(c(66))]

@evar cov(e1,e2) = c(67)
@evar cov(e1,e3) = c(68)
@evar cov(e1,e4) = c(69)
@evar cov(e2,e3) = c(70)
@evar cov(e2,e4) = c(71)
@evar cov(e3,e4) = c(72)"