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.