Hi, I could use some guidance from seasoned Gretl users. I am trying to
estimate the trend component of a univariate financial time series using an
unobserved components model and the Kalman Filter using the kalman command. I'm
new to Gretl and it's been some time since I've even looked at state space
models. Here are my equations:
Let x(t) be the univariate monthly financial time series data I have.
x(t) = w(t) + y(t) where w(t) is the trend and y(t) is the cycle
w(t) = x(t-1) + e(t)
y(t) = rho*y(t-1) + u(t)
e(t) and u(t) not correlated
In the notation of the Gretl users guide, I believe I have the following
matrices for the kalman command:
H = { 1 ; 1}
F = {1, 0; 0, rho}
Q = {var(e), 0; 0, var(u)}
I'm not sure what to do with the observation matrix -- this is where I'm stuck.
Also,should I specify statevar and obsvar as scalars instead? I have a
univariate time series, x(t). Once I have the system set up I could proceed to
estimate rho, var(e) and var(u), then calculate the trend forecasts.
Any guidance would be greatly appreciated.
