tag:blogger.com,1999:blog-3393033712226955105.post3543227432022395288..comments2016-06-20T19:13:49.124-07:00Comments on Econ Trash: SIM8: discrete time and continuous time state space system matricesTom Brownhttp://www.blogger.com/profile/17654184190478330946noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-3393033712226955105.post-46405742823870398962016-04-08T18:08:07.208-07:002016-04-08T18:08:07.208-07:00Hi Tom,
I edited my http://mechanicalmoney.blogsp...Hi Tom,<br /><br />I edited my http://mechanicalmoney.blogspot.com/p/mathjax.html<br /><br />I will try to understand Octave and write a matrix. That is next.<br /><br />Your equations for SIM as-is look pretty good to me! I keep referencing them as I try to translate my Equation. 10. Time for dinner.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-3393033712226955105.post-32254819039955913032016-04-08T15:11:53.987-07:002016-04-08T15:11:53.987-07:00Hi Roger,
I'm glad your wife is OK!
My matri...Hi Roger,<br />I'm glad your wife is OK! <br /><br />My matrices: if you undertake that project, I'd suggest you start with the discrete time case. For the continuous time case, I have an idea of what I need to change in mine to make the story more complete, but I haven't worked it all out yet. The discrete time case doesn't require any further thought... it's good as it stands.<br /><br />Also you'll note I could have introduced my old notation for X and saved a lot of repetition in those matrices. X is not the best name for it... especially now that I have a canonical $x$ in there... but it could do with some simplification.<br /><br />Good luck!Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-3393033712226955105.post-81400043500811851362016-04-08T14:54:12.762-07:002016-04-08T14:54:12.762-07:00ack from the doctor's trip for my wife. All is...ack from the doctor's trip for my wife. All is well, and she is better!<br /><br />"depending on whether you want to match the average rate over the associated discrete time sample period at the sample times,"<br /><br />OK, So far, I am intellectually following your idea that the only state we are updating is the wealth state. G just adds an increment to that state. My Master Equation starts from zero plus memory plus G. $$0 + G + \alpha 2 H_{-1} $$ It integrates those based on <br />$$\frac{1}{ \theta - \theta \alpha 1 + \alpha 1} $$ <br /><br />Now, I am going to read these beautiful matrices and try to place my Master Equation into matrix form. I am a long way from that goal.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-3393033712226955105.post-2807777022546664862016-04-08T08:41:59.424-07:002016-04-08T08:41:59.424-07:00I've already made a small but important update...I've already made a small but important update to $(6)$ and $(7)$ which I explain in the text immediately below $(7)$ regarding the indices and canonical state space form.<br /><br />There are more updates to come because I realize that the continuous time equations have different possible realizations... depending on whether you want to match the <i>average</i> rate over the associated discrete time sample period at the sample times, or if you want to report the instantaneous rate at a particular sample period. Most people who work with state space representations are interested in the instantaneous rate, however, SIM is geared toward the average rate over an associated discrete time sample period... thus I'm afraid some things will change. But if you stick with the discrete time equations for now you should be OK, and if nothing else the continuous time equations are approximately true (depending on what you want to do with them). More to come!Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-3393033712226955105.post-2803152430403993582016-04-08T08:31:30.914-07:002016-04-08T08:31:30.914-07:00Your results and presentation are absolutely beaut...Your results and presentation are absolutely beautiful. I am making progress, still putting the pieces together in my mind.<br /><br />I must take my wife to the doctor out of town. Will do a lot of thinking on the way.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-3393033712226955105.post-92155633478572268932016-04-08T06:06:15.956-07:002016-04-08T06:06:15.956-07:00I see your work. Beautiful!I see your work. Beautiful!Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.com