Hi, I am trying to estimate a dynamic factor model which allows for correlation between one of the observation error and the latent factor's error (as in Aruoba et al. (2016)'s GDPplus). I have 2 observable variables( price and retailP) and specified my basic model as:
y_t = μ + x_t + e_t
x_t=x_(t-1)+u_t
(u_t, e_t)`~N(0,Σ).
Σ is a 3X3 variance co-variance matrix whose elements are to be estimated. I am allowing for correlation between the observation error and the state error to account for non-classical measurement error in the price variable. In my state-space model, I specify the measurement equation with SV=0 and include e_1 and e_2 in the state vector to allow for the correlation. Attached is the code I have put together to estimate using dlm based on what I have learnt from the SSM DSGE tutorial and posts on this forum.
I have 2 extensions I need help with in RATS:
(1) How can I specify Σ to be time varying with the variation coming from GARCH effects in u_t (DNS-GARCH in Koopman, Siem Jan, Max IP Mallee, and Michel Van der Wel. "Analyzing the term structure of interest rates using the dynamic Nelson–Siegel model with time-varying parameters." Journal of Business & Economic Statistics 28.3 (2010): 329-343. available at https://papers.ssrn.com/sol3/papers.cfm ... id=1068861). The RATS replication code for the example in Durbin and Koopman textbook does not include the GARCH specification.
(2) How can I incorporate a break in the variance of the observation error for one of the observables (price)? I would like to test for a structural break in the measurement error of that variable in 2001.
Thank you in advance,
Bernadette