tag:blogger.com,1999:blog-6476989946886057900.post6971413837177941863..comments2020-05-17T14:13:07.488-07:00Comments on <small> <i> the </i> </small> Mechanical Money <small> <i> blog </i> </small>: A Master Equation for SIM Models Using the GDP Object DRAFTRoger Sparkshttp://www.blogger.com/profile/01734503500078064208noreply@blogger.comBlogger63125tag:blogger.com,1999:blog-6476989946886057900.post-83872044136460281552016-04-09T11:06:35.284-07:002016-04-09T11:06:35.284-07:00For my own convenience:
http://mechanicalmoney.bl...For my own convenience: <br /><a href="http://mechanicalmoney.blogspot.com/p/mathjax.html" rel="nofollow">http://mechanicalmoney.blogspot.com/p/mathjax.html</a>Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-13185344882721993292016-04-07T11:03:34.438-07:002016-04-07T11:03:34.438-07:00I saw and left some comments (and some block diagr...I saw and left some comments (and some block diagrams of my own).Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-83615009353415960682016-04-07T10:18:54.245-07:002016-04-07T10:18:54.245-07:00Tom, I created a new page displaying what I think ...Tom, I created a new page displaying what I think might be the state-space. Equation 10 looks to me like a regenerative amplifier with degenerative feedback.<br /><br />Maybe it can be found at <br />http://mechanicalmoney.blogspot.com/p/mathjax.html<br /><br />I have no idea of why the mathjax in the url.<br />Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-11101665123568206412016-04-07T10:02:33.790-07:002016-04-07T10:02:33.790-07:00This comment has been removed by the author.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-42419812001168256412016-04-06T21:31:24.455-07:002016-04-06T21:31:24.455-07:00... all in all, I like the Excel approach better. ...... all in all, I like the Excel approach better. I'd rather have the sheet protected. People can still download their own copy if they want to fix my formulas, and then email me a copy (or post a copy in Google, or on OneDrive that they let me download).<br /><br />It's not that I'm terribly worried what people will do, but I'd rather not have it slowly drift off into a non-functional sheet over time (if I'm not constantly monitoring it, say). Or maybe somebody will come along and erase everything and just write out in huge letters: "TOM BROWN SUCKS!!" ... Lol!<br /><br />hey, that gives me an idea..... who do I know that has a shared Google Docs sheet? Hmmm.... ;)Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-24242940396829439502016-04-06T21:27:18.728-07:002016-04-06T21:27:18.728-07:00... a drawback of the Excel approach is that nobod...... a drawback of the Excel approach is that nobody can help you fix errors with it, unless you grant them some kind of special access to your "OneDrive" account. Also, they only have limited controls through the web-page: they cannot see or change formulas in cells, only the values (at most).Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-86276689937527540042016-04-06T21:25:12.219-07:002016-04-06T21:25:12.219-07:00I left more than one comment. =) (but all in the s...I left more than one comment. =) (but all in the same place).Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-66753568853078344452016-04-06T20:25:43.219-07:002016-04-06T20:25:43.219-07:00I found the comment and you are right. There are I...I found the comment and you are right. There are IF(x,x,x) in two rows but Offset, much to my chagrin. Another thing to fix. Glad it works. Next, get better ways to protect the sheet or go to Excel. More on this tomorrow.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-26040465475813297592016-04-06T20:11:16.556-07:002016-04-06T20:11:16.556-07:00... that's the only drawback to the Google Doc...... that's the only drawback to the Google Docs approach: strangers or no-good-nicks or people like me can wander in off the internet and mess up your sheet! With Excel, each person viewing the sheet has their own personal copy and their edits do not change the original or what anybody else will see. If they mess up their own copy, they just need to refresh their browser to get an original copy back.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-32925043354646322922016-04-06T20:07:05.016-07:002016-04-06T20:07:05.016-07:00Hi Roger, yes I can see it and it works. I left a ...Hi Roger, yes I can see it and it works. I left a couple of messages in there for you... see if you can find them! =)Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-67045067914667902482016-04-06T20:02:25.239-07:002016-04-06T20:02:25.239-07:00The spreadsheet link seems to work from here. I se...The spreadsheet link seems to work from here. I see you need to go to sheet 1 (it initially goes to sheet 4) and it is a little slow to load.<br /><br />I will fix it or get a workaround if you can see it.<br /><br />Something to sleep on. I think Eq. 10 is like a controlled regenerative stage. It has 5 inputs and one output. The output GDP is the stored result. Linear system block A is the regeneration control. A second external block A updates a memory containing wealth information, using the GDP output. I think the GDP output is the only information need to fill out the rest of SFC SIM parameters.<br /><br />The link to the state space page provides entry to a lot more information. I will study all of this much more.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-77598312288820021502016-04-06T19:13:18.107-07:002016-04-06T19:13:18.107-07:00Tom, Can you see the spreadsheet here?
https://do...Tom, Can you see the spreadsheet here?<br /><br />https://docs.google.com/spreadsheets/d/1tOb_cgEy1twrDzhSpaJek75JLXolF1QQXX2ndGGdmqs/edit?usp=sharing<br /><br />It seemed to transfer from Excel to Google Sheet reasonably OK. I see the check box is missing but there is a zero in the next column. Change the zero to 1 and the jump works.<br /><br />I could also put the Excel file on my web site but I have not accessed that for a couple of years. Need to find the password and more.<br /><br />Could also get a Microsoft online account. Trying the free stuff first.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-78195367901959994802016-04-06T17:51:11.655-07:002016-04-06T17:51:11.655-07:00Roger, here's a page I put up about the Z-tran...Roger, <a href="http://banking-discussion.blogspot.com/p/z-transform.html" rel="nofollow">here's a page I put up about the Z-transform</a>, including a Matlab script (that hopefully runs in Octave) which shows you an example of how it's calculate for a finite length sequence. The Z-transform of finite length sequences converge in the whole Z-plane (i.e. their ROC is the entire plane).<br /><br />It looks long, but it's VERY simple. Most of the script has to do with making the figures and console output look nice. Enjoy!Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-35760724264081357302016-04-06T15:44:52.454-07:002016-04-06T15:44:52.454-07:00... and D = 0 (it's completely missing), which...... and D = 0 (it's completely missing), which is actually pretty typical, as I've pointed out before. For your model (and for SIM) you'll need a D though!Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-71795003443197548952016-04-06T15:41:33.205-07:002016-04-06T15:41:33.205-07:00... Oh, and z for y (like I have it: as a noise co...... Oh, and z for y (like I have it: as a noise corrupted y).Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-77584786437162892512016-04-06T15:40:38.233-07:002016-04-06T15:40:38.233-07:00And look here: the state space equations for a Kal...And look here: <a href="https://en.wikipedia.org/wiki/Kalman_filter#Kalman.E2.80.93Bucy_filter" rel="nofollow">the state space equations for a Kalman-Bucy filter</a> (where the noises are important), uses F or A and H for C, with the measurement noise (v) covariance being R and the process noise (w) covariance being Q. Lol... oh well. The main thing is not the names, but the form. =)Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-51941049755275055472016-04-06T15:33:21.053-07:002016-04-06T15:33:21.053-07:00Also, bear in mind that Brian Romanchuk's pres...Also, bear in mind that Brian Romanchuk's presentation of the "cannonical form" of a state space model is actually slightly different. He's folding into his presentation his method for avoiding algebra on the SFC accounting equations. The Matlab and Wikipedia pages I link to above are closer to what you'll find in most literature.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-37769528213693747372016-04-06T15:28:52.349-07:002016-04-06T15:28:52.349-07:00Actually, here's another Matlab page where the...Actually, <a href="http://www.mathworks.com/help/ident/ug/identifying-state-space-models-with-independent-process-and-measurement-noise.html" rel="nofollow">here's another Matlab page</a> where they write down the cannonical model, but instead of $\Psi$ which would cause the noise process $\Psi v$ to have covariance $E[ \Psi v v^T \Psi^T] = \Psi \Psi^T$ given that $v$ is AWGN with unity covariance $E[v v^T] = I$, they just say that $E[v v^T] = R_2$. I find different authors diverge on how to name and treat the noise sequences and their covariances, but most stick to x, y, u and A, B, C and D.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-26811750005855579152016-04-06T15:27:49.798-07:002016-04-06T15:27:49.798-07:00This comment has been removed by the author.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-36351410457253825332016-04-06T14:59:16.056-07:002016-04-06T14:59:16.056-07:00"Also note the role of the three vectors x, y..."Also note the role of the three vectors x, y and z (potentially of different dimensions)."<br /><br />Should have been:<br /><br />"Also note the role of the three vectors x, y and u (potentially of different dimensions)."<br /><br />There is a z too that's often used: it usually represents an output (y) corrupted with measurement noise:<br /><br />$$z = y + \Psi v$$<br /><br />Where v is additive white Gaussian noise.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-60391368612254503452016-04-06T14:56:18.049-07:002016-04-06T14:56:18.049-07:00Roger, here's Wikipedia on state space represe...Roger, here's Wikipedia on state space representations:<br /><a href="https://en.wikipedia.org/wiki/State-space_representation" rel="nofollow">https://en.wikipedia.org/wiki/State-space_representation</a><br /><br />As you can see the really do use A, B, C and D. Also, that's precisely what Matlab and Octave expect:<br /><br /><a href="http://www.mathworks.com/help/control/ref/ss.html" rel="nofollow">Matlab's ss() command.</a><br /><br />Also note the role of the three vectors x, y and z (potentially of different dimensions).Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-7306552553160839632016-04-06T14:52:04.360-07:002016-04-06T14:52:04.360-07:00Let's try this:
http://mechanicalmoney.blogspo...Let's try this:<br /><a href="http://mechanicalmoney.blogspot.com/p/this-is-my-testing-page-not-for-public.html" rel="nofollow">http://mechanicalmoney.blogspot.com/p/this-is-my-testing-page-not-for-public.html</a>Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-25938685938984992042016-04-06T14:50:52.234-07:002016-04-06T14:50:52.234-07:00"Say, would it be alright to put your name in..."Say, would it be alright to put your name in the post for acknowledgement when I finally convert it from DRAFT?"<br /><br />Sure!<br /><br />... and you're right: I see no sign of your test page other than through the link you give there. Nice!... maybe it defaults to NOT including a menu of pages at the top (like in my old blog).<br /><br />Well done Roger: you've got a lot accomplished!<br /><br />Let's see if I can make a link to it:<br /><a href="mechanicalmoney.blogspot.com/p/this-is-my-testing-page-not-for-public.html" rel="nofollow">mechanicalmoney.blogspot.com/p/this-is-my-testing-page-not-for-public.html</a>Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-70052103266488086602016-04-06T14:47:29.861-07:002016-04-06T14:47:29.861-07:00Brian writes "x(t+1)=Ax(t)+Bu^(t),x(0)=x0.
x(...Brian writes "x(t+1)=Ax(t)+Bu^(t),x(0)=x0.<br />x(t+1)=Ax(t)+Bu^(t),x(0)=x0.<br />In this case, xx is a vector of variables, residing in RnRn. For those of you who are unfamiliar with matrix notation (or purged the concept from memory), that means we are stacking up nn time series variables into a single object. Using economic lingo, x(t)x(t) are the endogenous variables, and the vector u^(t)u^(t) is the vector of exogenous variables ("inputs")."<br /><br />OH, I think the light just went on. I need to think this through however.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6476989946886057900.post-63448587041030522962016-04-06T14:36:20.575-07:002016-04-06T14:36:20.575-07:00Wow, it was up for very few minutes!
I think I ha...Wow, it was up for very few minutes!<br /><br />I think I have something figured out. If I go to the blogger Overview Page, it has an option "Pages". I had no pages but did have post. I now think I have a page that does not post, even though I published the page. The link is <a href="#editor/target=page;pageID=939930961207581596;onPublishedMenu=pages;onClosedMenu=pages;postNum=0;src=pagename" rel="nofollow">Mechanical Test Page</a><br /><br />Hmmm, I had to modify the href, removed the class keyword so that preview would accept. That may wreck the link. I could include the html.<br /><br />http://mechanicalmoney.blogspot.com/p/this-is-my-testing-page-not-for-public.html<br /><br />I do not see this page on the post list. I find it when I use the link.<br /><br />If you are at the test page, you should see a crude picture of transaction GDP. I am still trying to understand Z-transforms and the way it is written. I wonder if we and Brian all have the same SFC model goal. The picture has is still in the "think" stage so watch out for intellectual noise.<br /><br />Say, would it be alright to put your name in the post for acknowledgement when I finally convert it from DRAFT?Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.com