I am trying to make the following Kalman filter equations work and therefore
produce their graphs.
v_t=y_t - a_t
a_t+1=a_t+K_t*v_t
F_t=P_t+sigma.squared.epsilon
P_t+1=P_t*(1-K_t)+sigma.squared.eta
K_t=P_t/F_t
Given:
a_1=0,P_1=10^7,sigma.squared.epsilon=15099,
sigma.squared.eta=1469.1
I have attached my code,which of course doesnt work.It produces NAs for the
Fs,Ks and the a.
Can somebody tell me please what am I doing wrong in this loop?
Why doesnt this loop work as it should be;to produce plots of a declining
filtered state variance(P_t),prediction errors(v_t),and a declining prediction
variance(F_t)?
Also,how can I construct and plot the 90% confidence intervals around a_t?
Thanks for your help and look forward.
Leonard
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y<-(Nile)
n.y<-length(y)
P<-numeric(n.y)
a<-numeric(n.y)
i<-y
P[1]<-10000000
a[1]<-0
n<-100
sigma.2.epsilon<-15099
sigma.2.eta<-1469.1
nv <- matrix(nrow=100, ncol=1)
F1<-P[1]+sigma.2.epsilon
K <-P[1]/F1
for (i in 2:n-1){
P[i+1]<-P[i]*(1-K[i])+sigma.2.eta
F[i]<-P[i]+sigma.2.epsilon
K[i]<-P[i]/F[i]
nv[i]<-y[i]-a[i]
a[i+1] <-a[i]+K[i]*nv[i]
}______________________________________________
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