Alternative solutions for Laubach & Williams(2003)

[hardmann]

Dear Tom:
We have rewritten the model and code for Laubach & Williams(2003). In pure trend-cycles decomposition, both trend and cycle should be specified as states, in general, trend is local trend or local level with drift, and cycles is AR(2) structure. In L&W(2003) paper, however, gap or cycle is indirectly derived by potential trend, ystar. We constructed the model with natural notation on state space. By explicitly using the trend (Tau)and cycle (c), we put IS equation as states equation, and put the y=tau+c constrains as measurement equation. Through coding, we reserve the initialization and peg same parameter. We did not change the others. In origin codes of Winrats, we merely add suffix to the states variables for three stages to distinguish them and graph them.
By comparing the result of gap and AIC, SBC at three stages, the rewritten model seems superior to the origin one, however, the estimation of Natural rate of interest is inferior to the origin.

We do such model for aiming at two aims. Firstly, we guess the natural expression of model is easy to understand and applied. Second, if the trend and cycle components is constructed as states, them can be extend mixed frequent setting. Our ultimate goal is to estimate monthly even more high frequent natural rate of interest.

Pls Tom to guide and help us.
By the way, pls view our another question. We add our newly post and codes with two years old question. Thanks again.
viewtopic.php?f=26&t=3342#p18344
Best Regard
Hardmann