Sunday, May 24, 2015

My favorite sequence

Sum of (2/3)^n and sum of (1/3)^N

These power series sums make 2 and 1/2, so we have:

cosh^2-sinh^2 = 3/2  Spare capacity

I call this the optimum queuing model, it keep two queues. One queue has 1 or 2 in line at a time, the other 0 or 1. Phi^16 = (2/3)^19. Npw Phi is just a numberical tool, in this case it stands for the ratio of two Fibonacci numbers.

Anyway, to my thinking, 2/3 and 1/3 are the Boson and Fermion exchange rates whne there is no motion.  These are the conversion ratios when the bubbles are separated into the cold and hot positions of Wythoff.  For Fermions, the cold spots out number hot spots 2 to 1. Two times as many bubbles have no desire to go overlapping.

Now the 13th Fibonacci number is 377, about where the spare capacity is near the fine structure.  That should not surprise us, the Hyperbolics as simply a useful too to manage power series.  And Phi is just an estimation tool. So any reduced physics model will have lots of matches to some power series tool. But the adapted bandwidth requires sinh = cosh', and visa verso so it supports the impedance model. The tool is built around bandwidth adapted systems, two period constraint.

How does the system make (2/3)^n match (1/3)^n?  The 1/3 and 2/3 series shift, that makes charge, and they  become an additive series.

Republican Communist Party watch

(Bloomberg) -- Republicans in the U.S. House and Senate say their budget proposals add up. It takes some creative math and logic to make that true.
The plans unveiled this week call for the U.S. government to collect about $2 trillion in taxes in the next decade that Republicans have little or no intention of collecting. Some of that revenue would come straight from taxes to pay for Obamacare -- which they want to repeal.
Republicans also gloss over details of where they’d cut more than $5 trillion to balance the books. Senate Budget Chairman Mike Enzi’s plan cuts $430 billion from Medicare without saying how. House Budget Chairman Tom Price’s proposal includes $1 trillion in “other mandatory” reductions that aren’t entirely laid out.
Budget analysts are criticizing the approach.
“While the goals put forward by the budget resolution are praiseworthy, the details are in some ways unrealistic and unspecified,” Maya MacGuineas, president of the bipartisan Committee for a Responsible Federal Budget, based in Washington, said in a statement.
The House proposal includes about $94 billion for a special war-funding account that isn’t subject to spending limits set by Congress in 2011. The Senate plan includes $58 billion in war funding, the same amount requested by President Barack Obama.
We balanced it under Bill Clinton. Put the sequester back, that was working fine.

Traversing from hyperbolics to yield curve

This part is mainly to clear things up because of the annoying habit of looking at the tanh curve and seeing it is shaped like a yield curve, and that is confusing.

I made a fake yield curve, out of scale, mainly to get the axis and units aligned. I converted hyperbolic angle, x axis,  to term length.  And the curve is not hyperbolic shaped because the hyperbolic angle is inverted and flipped, both.   I used liquidity 1.5 as that seems to be the liquidity for the real curve up to the six year term. But I am still working that.

When liabilities to assets are near one, that is the short end and rates are low.  Loan terms are short, no term premium so rates are low and liabilities high.  So, long term loan, the market carries more assets against the loan, large down payments required. I think I have this.

Saturday, May 23, 2015

Hillary created ISIS?

This report says so. But I tried to link through to real evidence and got not much more than innuendo.

What Secretary of State Hillary Dingbat created was chaos, chaos everywhere she went. That is all she does, create chaos.  Look over her entire career, almost all of it, from first lady to presidential candidate,  Dingbat Chaos. She is clueless, going through life reading from a script.

Liquidity and Forex trading

Zero Hedge brings it up. How much liquidity should a bot retain? Generally Phi if the market is adapting perfectly.  So for any two period model, a currency value may grow by G^2 and shrink by S^2, so G^2- S^2 = Phi.  That gives the market enough liquidity to pass the 'map' around as circumstances change.

Here is my thinking, take it or leave it.

1) All the moves we see in the markets are one period moves designed to stabilize a two period plan. This includes the bots.  If that were not the case then the market would blow up.

2) When a currency is gaining value then the market is doing the tanh function and the tanh flow constraints apply. Tanh gives you the down move over the up move and it should be less than one.  The probability of that trade pair is given by (1/2)* tanh'', taken as positive. The most likely trades are Pi/4 down and Phi*Pi/4 up.  But the bot should track the probability curve and bet to make that valid.

3) When a currency is losing value then  the market is doing the coth function, and the most probable trades are around 1/2 up and sqrt(5)/2 down.  Butuse the (1/2)* coth'' curve, taken positive, for the most probable trades.

4) There is twice the market activity up then there is down, I think.  This is the  boson uo and fermion down thing.

5) I am not sure how to scale these to real currency values.  Phi should be the signal to noise power ratio, if this market is adapting. Measure that SNR in units of the currency and you can scale all this.

Frequency falls as the hyperbolic angle drops, is my latest contorted thinking, but I still am a bit disoriented about mapping the hyperbolics to real markets. But, once the no arbitrage bots protect everyone's trade, then high frequency spoofing will not work.  Zero Hedge wants the world to go back to fundamentals, the no arbitrage bots do that because the recognize only new information.

Sorting vectors

I have a collect of N vectors, of arbitrary dimension,k. So they can be arranged as a k column by N row matrix. I want to sort them by significance, the vectors which most precisely describe the collect sorted higher.

Step one, find the mean/variance of each column. The column with the highest m/variance is the more significant, it has the lease noise. I pick some base b such that the logb(1+m^2/var) for all columns that makes the most significant column have a log at least one great then the rest.  I take the log of each element in the most significant column.I sort the rows based on that column. I split the matrix in two groups depending on whether the most significant bit is set in that column.

I then repeat this process for each of the two resulting matrices until there is no more sorting to do. Does this work?

Applying hyperbolics to the treasury curve

I simply took the existing rates and their log. Then I subtract one rate from the other. The hyperbolic angle is largest at the short end. I always get this mixed up, but now that I got off my rear and did the work it makes more sense.  The largest hyperbolic angle is pi()/2, so we see that the first three rates are split evenly by some delta of the hyperbolic angle, they have the same liquidity. Then going past the knee of the curve, liquidity changes. But this is clear from looking at the curve, it is linear up to the knee. All this proves is that two period planning is likely the norm and that we change the market liquidity at the knee of the curve. It also trains me to orient myself better when trying to match hyperbolics to any aggregate system, its not clear how to orient the thing until one actually works through a data sample.

Rate log diff
0.200 1.349 -0.221
0.610 1.107 -0.242
1.560 0.903 -0.204
2.210 0.828 -0.076
2.980 0.763 -0.065

Getting oriented then.
Hyperbolic angle is large at the short end of the curve, rates lower and loan/deposit close to one.  Loan/deposit decreases at the long end of the curve. But these are the aggregate numbers for the lending market. The problem is when lenders and borrowers individually deviate from the two period model.  DC, for example. It acts like a member banks, but it segments the members banks into itself with all the loans and the real banks that have all the deposits. Then at the long end, DC appears again, with all the loans and most of the deposits held by wealth.  G fouls the whole mess up and causes liquidity crashes, the markets becomes unstable.  

Friday, May 22, 2015

Liquidity and interest rates

Consider two cased, fixed term, non-tradeable deposit certificates and loan. And the other case, tradeable deposits and loans.

The non-tradable paper has a fixed market liquidity which is set to the standard value of 1.0.  One means one transaction, essentially.  This is the case where neither the lender nor borrower expects any material changes in the economy, a fixed term non liquid market. At the end of the period, the depositor demands principal and interest, and visa versa for the lender.  The both have to prepare to make the money good.  Hence, the two period planning model. Lender and depositor get one period to adjust their cash in preparation to the two period demand, this is the basic rule of adapted statistics.

Let's define an index, m, which identifies an ordering of markets for which loans and deposits are made with liquidity 1. Set deposits to D, loans to L, then we have:

D(m) is the amount due, principal and interest, over one period in market m. Do the same for loans, L(m). Then we apply the two [period model and take the derivative with respect to a change in markets.

D(m)^2 - L(m)^2 = 1, and its derivative, D(m)D'(m) - L(m)L'(m) = 0.

All this says is that we are dealing with markets having liquidity constant 1, so this differential must be zero.  And we see that D' = L and L'=D. Regardless of the liquidity value, stable markets have constant liquidity. So we get a standard result if the market liquidity is constant and two period planing is in effect.

The form of the deposits and loans

 We are already hyperbolic, lets look:

deposit value = (e^m+1/e^m)/2 and loan value is (e^m-1/e^m)/2
So what is going on here is maintaining liquidity. Over one period we want the deposits to earn 1/2 of the liquidity requirement and loans should retain 1/2 unit of liquidity. So, in one period, we have a half unit earned on deposits and a half unit retained on borrowings. Thus, the required liquidity in an adapted network is met.

Next we deal with liquidity different than one. This is the case when the network has to adapt. Let the adaption liquidity be some Q. Then we have:
D^2-L^2 = Q^2.   So in one period, D has to earn Q/2 and loans reserve Q/2. But our derivative still has to work, and they do according to my wxMaxima machine.

What are rates and balances?

D is the one period value, so:

b(1+r) = (e^m + Q*e^-m)* 1/2 = 1/2 * e^m *(1+Q * e^(-2m))

r= Q* e^(-2m)

b = 1/2 * sqrt(Q/r), with likely math errors 

So there is a fixed relationship between liquidity required and rates for any market m.   For loans, use reverse time like they do with anti-electron or like cash in advance. I will work it later.

So, term period is not known, but there is a frequency relationship between the currency banker at m=1 and the rest of the markets.   And for any given m, Q, the liquidity is a scale factor to the value of deposits and loans. That is, any quantity of deposits and loan values can be simply accumulated as a batch of unitary loans, so scale does not yet come into play. But the number of deposit/loan pairs at any given m, relative to another m, will be constricted by the flow conditions. The probability of a deposit/lona pari across all m have to be one, and that proability is inherent in the loan/deposit ratios at any m.

Did QE lead to faster NGDP growth?

The blue line is growth in NGDP, the red is the Fed bond portfolio. I see NGDP growth stuck around 3%, maybe the Fed added a quarter point to that number.

Jeb Bush caught in a lie

Angry Bear: Questioned by a voter inside a sports bar about whether there is “space” between himself and his older brother on any issues, Bush offered a clear critique.
“Are there differences? Yeah, I mean, sure,” Bush said. “I think that in Washington during my brother’s time, Republicans spent too much money. I think he could have used the veto power — he didn’t have line-item veto power, but he could have brought budget discipline to Washington, D.C. That seems kind of quaint right now given the fact that after he left, budget deficits and spending just like lit up astronomically. But having constraints on spending across the board during his time would have been a good thing.”

Deficit when Obama took over was about 9%, after adjusting for Obama;s stimulus act. After it increased a bit, Obam has reduced it steadily.
Jebb Bus is a liar.