Hello, now here is my code for the seasonal state space model. The forecasting performance is okay, but the p-values of the coefficients are not as expected.
Any suggestions?
series y=m+g+e
m=trend, g=seasonality, e=irregular
seasonality is modeled by using trigonometric terms. I think the starting values might be a problem. But i am not sure. If i log the series, i get the "coefficients are not unique"-Warning and p-values are not available.....
Thanks in advance!
Code: Select all
'Variables
!s=4
'create lambdas
for !j=1 to !s/2
scalar lambda!j=@acos(-1)*2*!j/!s
next
'state space model
sspace ss_{%0}
ss_{%0}.append @signal {%0}=sv1+(sv3+sv5)+[var=exp(c(1))]
'trend
ss_{%0}.append @state sv1=sv1(-1)+sv2(-1)+[var=exp(c(2))]
ss_{%0}.append @state sv2=sv2(-1)+[var=exp(c(3))]
'seasonality
ss_{%0}.append @state sv3=@cos(lambda1)*sv3(-1)+@sin(lambda1)*sv4(-1)+[var=exp(c(4))]
ss_{%0}.append @state sv4=(-1)*@sin(lambda1)*sv3(-1)+@cos(lambda1)*sv4(-1)+[var=exp(c(5))]
ss_{%0}.append @state sv5=@cos(lambda2)*sv5(-1)+[var=exp(c(6))]
'initial values
c(1)=@var(log({%0}))
c(2)=0
c(3)=0
c(4)=0
c(5)=0
c(6)=0
'Estimation
smpl @first 2007q4
ss_{%0}.ml(showopts,c=1e-1,m=1000)
show ss_{%0}.output
'Forecasting
smpl @all
series {%0}_ss
for !i = 0 to 7
smpl 2008q1+!i 2009q4
ss_{%0}.forecast @SIGNAL ss_temp
{%0}_ss= ss_temp
next
smpl @all
) the same specification as Koopman and Ooms (2002), http://www.econometricsociety.org/meetings/esem02/cdrom/papers/1267/KoopmanOoms2002.pdf (see Chapter 2).