Earth Quake Frequency

After the Asian tsunami in 2003 had a quick look at sun-earth relationship with regards to quakes as this one happened near the solstice. There is no obvious correlation.

However getting a bit more into it after the Tohoku Earthquake I just looked at the angle between the Sun and Moon.

The chance of a quake almost doubles when the Sun-Moon angle is 70 degrees.

This is a number I am rather familiar with after all the Phi stuff earlier in the year. It is 1/5th a circle and the angle of a pentagon whose inner pentagram has sides of ratio of Phi.

The data in the graphs is upto 2003. Checking the angle of Sun and Moon on the fateful Friday it was 73 degrees!

What does come out of the brief look today is that there is no correlation between the longitude of quakes on the earth surface and the position of either sun or moon (not looked at together). There is also no correlation with distance so the recent Super-Moon is a coincidence.

Discovered that the Sun's gravity accounts for 44% of the tidal energy and the Moon 56%. The moon creates a 30cm Lithosphere bulge by itself so as it passes over, the ground rises 1/3 metre! Sun and moon combined not sure how to work it out. Is its simply 79% more i.e. a 54cm bulge - probably not linear but that is a heck of a massaging of plates!

There is certainly much to know (this is just a day spent finding code to do the planet predictions) enormous thanks to Keith for the functions:

'Astro-functions

'Keith@xylem.demon.co.uk

'http://www.xylem.demon.co.uk/kepler/

'http://www.stargazing.net/kepler/astrovba2.html

I do wonder why the scientific community always say they know nothing in this field:~ Weather forecasters have a much more complex job and at least they try.

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Actually if there is a grouping, it suggests more Earth Quakes at closest approach to sun (late Dec-early Jan at moment) + when the Moon is farthest away. The graph on left shows frequency of major earthquakes against distance of Sun (the peak would be much more obvious if the x-axis was wrapped around and started in mid scale!). The graph on right shows distance of moon on x-axis (I don't get the units of this function) and distance of Sun (again relative to mean distance = 1). There is a clear increase in frequency as the moon moves away from the Earth! Combined with the Sun this means that mid-winter and distant moon make the most likely combination for an Earthquake, combined with a Sun-Moon angle of 70 degrees which is a 1/3 Full/Empty moon.

Looking Moon phase during Earth-quakes here's an odd coincidence: when the angle (from Earth) between Moon and Sun is 70degs (peak Earthquake angle), the angle (from Moon) between Sun and Earth is 109.86 degrees. The Moon phase is then 0.33 (1/3 illuminated or 1/3 dark) using the equation: phase = (1 + Cos(angle))/2. Now the coincidence is that 0 (full moon) & 109.47 (1/3 moon) are the only two angles where the size of the projection of the Earth vector into the Sun vector (from the Moon) is the same ratio as the Phase of the Moon! ie. |Cos(angle)| = (1 + Cos(angle))/2. What significance who knows.

This is to say that the projection of the Moon-Earth Vector (e) in the Moon-Sun vector (s)

as a proportion of (e) is the same ratio as the moon phase when t=0 (fullmoon) or t=189.47 (1/3 moon) and this corresponds to a moon-sun angle from Earth of about 70 degress which statistically is by far the most likely time for earthquakes.

What possible reason?

Planets, Fractal, Phi and Stockmarkets

Following up on the Ouroboros stuff from ages ago, which is related to the SRH thread, and through an article on Alchemy I came upon the presence of Phi in the planetary orbits. Odd I think and am trying to explain that becauise it is also used in charting stock markets. It is commented already that stock markets show fractal geometry, and Phi is the limit of the relationship between adjacent numbers in the Fibonnaci Sequence - a sequence that is gained by recursion i.e. fractal! Consider two systems A and B which proceed by adding the value of the other system - this is the Fib sequence. A and B can start at any value (as long at they are different).

A 10 24 etc
B 14 38

They will come into Phi relationship ... why? Algebraically it is obvious:

B(n) / A(n) = [ B(n-1) + A(n) ] / A(n) = B(n-1)/A(n) + 1 (ok not quite I've got this in notes will update)

Anyway looking further this is interesting and I note it for reading later:
http://www.cyberalley.com/G-Home/R&D/R&D5/FofL12.html

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http://www.ermanometry.com/

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Funny how everything appears to fit together ... or is this an illusion because I want it so? Actually I don't want it so because if Phi is this fundamantal then it will end up explaining things rather than being explained!

http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html

So it seems that in iterative processes the repeating units come into Phi relationship *for some reason*. This link describes it as "self-reference" - I don't call it self reference because it isn't. A large structure being composed of structures "similar" at many scales is only "self" in the sense of "similar". Altho I must conceed that a set which is made of copies of that set at a smaller scale is more extraordinary than one that is made from dissimilar material. This really questions what we mean by "self". What we don't mean (a la Buddha) is a material existing thing called self. Fractals actually illustrate this "self" that is built from "copies" of "itself", and so not self and self at the same time.

But why Phi?

Web site here were the writer seems a little carried away with the patterns. If there was no pattern that itself would be amazing. It is Wolfram versus Caitin on whether the universe is full of information or whether the apparent diversity has underlying rules. I part company on ths page and this statement "There is no natural explanation for these unusual relationships" [http://solargeometry.com/34power.htm]. I reckon there is a very good reason. 2 options. Either:

(1) the planets formed in this relationship and it is a feature of the fractal collison and amassing of dust in the emryonic nebula + the expulsion of massive rocks that were too excentric and out of phase with the system. OR

(2) over time the planets have evolved into this relationship. Evidence for this would be that the inner planets (with more revolutions and periods of evolution) have tighter relationships.

Some things to note. All the planets bar Earth are in a 2*Phi relationship. Mars is the most deviant. And there is a missing planet (from the pattern) between Mars and Jupiter, where instead is the asteroid belt.

Jupiter, Saturn and Uranus are massive and it seems likely to me that the planet that formed immediately inside jupiter's orbit suffered some catastrophe and either never formed properly, was broken up by the gravity of Jupiter or there was some massive early collision creating the asteroid belt. Mars, which is incredibly light, will be hugely affected by Jupiter and aided by early collisons from the drama in the asteroid belt has a distorted orbit.

However such speculation leads no closer to why Phi.

The inner planets are in almost circular orbits. This is most likely the influence of Jupiter which I understand would accentuate any eccentric orbits and eventually fling the planet from the system. By simple evolution only circular orbits exist. Given radius from the Sun, and assuming nearly circular orbits, the possible velocity and therefore orbit period are hugely constrained for the planets. I need develop my calculus a bit before describing that in detail.

Then it remains only to find out why only certain radiuses from the Sun are favoured for planet formation and stability.

I expect the iterative dynamics to be something of the form Sqrt(x+1) = x or x = 1/(x-1) both of which converge on Phi...

Then I have a demonstration of my hunch that a similar iteration exists in the Stock Market game mentioned a few posts ago. After all the stock price is what speculators base there trading on, and their trading affects the stock price so there is an iterative system and ergo it will show fractal geometry (with patterns feeding back through the system at scale) with stable points existing at solutions to these interations ... like Phi.

Meaning of Life

I have finally started to come to terms with the answer to this question.

The answer is that there is no meaning or purpose. This is not an easy thing to accept however: this is the real problem. The reason why we can't accept it is that we have large amounts of energy to expend, and many desires to satisfy so that while our bodies are poised ready to floor the accelerator in pursuit of some goal, our minds discover with a little investigation that "goals" are not so one sided. An example is that of war. I watched again with pleasure "The Guns of Navarone" yesterday. The pursuit of that goal, and the licence that goal gives the protagonists to floor-the-accelerator (argued out between Peck and Niven many times), rouses the passions and the energy and gives us a view of the Noble Quest that goes back to the Age of Chivalry and probably beyond. I note, as an aside, Peck remarks about his "stupid Anglo-Saxon decency" (while talking to A. Quayle on the boat) and indeed I am beginning to realise this concept that underpins the British concept of the Gentleman is quite unique in the world - it may have existed in India in the concept of the Aryan (as discussed in this blog) but I'm beginning to see that it is all but lost everywhere.

Now the heart and the body rejoice in having all this excitement and useful application, but the mind quickly sees through it. For starters what is a celebration of a goal well done in the film is actually not even the start of the mission to over throw the Nazi occupation of the islands which the men on board the battle cruisers will have to under take. All could still fail! The other more obvious problem in the narrative (and argued at length in this blog) is that the Nazi are trying to do exactly the same against the Allies. A successful story for them is where lots of allies are killed and strategic land gained. It is simply that the narrative puts us on a particular side that the story can be a fulfilling ending; told from the Nazi side, exactly the same story is a crushing blow and very frustrating. The mind who can see both sides thus challenges the body which only wants to see one side. So challenged the mind sees that the body can never be satisfied except through wilful ignorance. This is the state of war, and of much human activity in general.

Another example that comes to mind is the saving of people's lives. We may give someone an extra 10 years, 20years or more through saving them, but the mind realises that death is not something we can run from for ever, it is integral to being alive - you can't have one without the other. So saving a life is only a matter of quantity not of quality, and one might argue that really facing death is a better approach than trying to escape it.

So the mind always leads the body back to the cross-roads of indecision and inaction. This all seems very depressing and frustrating, and that is what has hampered by progress in the question. What is obvious then is the next question what is the meaning of the question? I don't mean how do we understand the question, but rather why should it matter that there is no answer? Why do we struggle with the realisation that struggle never achieved anything!

So eventually the dawning realisation that what seems so catastrophic and depressing about life actually applies to the very depression and pointlessness itself and cancels it out. When the struggle for "something" has evaporated then there is simply stillness. No longer is there even the struggle to find that something, or even the desire to have a something at all. Is this what Buddha means by the "nothing".

Standing at the centre, which is where we always appear to be even after a long journey, then we are free to gaze out on the never changing world; all movements never shift us from the centre so nothing ever does anything or amounts to anything... and even that struggle we once had to measure the changes caused by our actions, or the movement and significance of our lives, or to find a direction in which to travel with full energy and haste, that struggle ends.

What is the Sanskrit for "struggle" it seems quite important. Dukkha might be the frustration at things never being quite right, but what of the struggle that we embark on the end dukkha through our ignorance of the Dharma (Law of reality, Word or Logos)? Does this suggest I have it wrong, or simply not read things right?

So the meaning of life is found when we stop struggling. It is that old parable (told by P. Coelho in the Alchemist) that the gold of our lives lies at home, at the start of the journey that we will return back to with wisdom. That parable shows that the very search for " a meaning to life" actually equips us with the wisdom that we had lost and which began the journey, the wisdom that tells us to look at "home", or the centre, from where we shifted in ignorance in the first place. The Mount Kilash from which Shiva almost never stirs. Home as notes in the Blog and known to me long before I started writing this is the issue that lies in all human hearts. I first wrote that in an analysis of caving where caving was seen as an allegory for the return home (caves having been amongst the first homes used by man). Where we mostly end up in family homes, this itself is an allegory for the final stage of finding the family and the home within ourselves.

Once we are at home, then what? What is the working day like for the person who really comes home to his soul, and not just his wife and his bed, at the end of the day? This is what I cannot quite grasp. I have a glimpse in writing the above that while a doctor may be mostly wasting his time creating more years for the ageing, if he spends his time instead leading people toward wisdom and their own souls, and gives them those extra years in order to do that, then his day is well spent. It is the cloud of materialism that blinds the sun which is often the problem. A problem is reduced to a material series of facts and equations and thus "solved". An ill person is mended and then discharged. Yet the real illness probably still continues both in the doctor and the patient, that the point here wasn't the dying, but rather the fear of death. In 30 years time the patient may return and this time there is nothing the doctor can do; neither person can run from the reality this time and then death must be faced. This is not to say that people shouldn't seek to live, that is an absurd thought since we do live already so why change it, it is that it is better to die in touch with our soul than to live in fear of it. I write this as much for myself as anyone who reads it. The doctors priority is really to bring the patient to accept the nature of their body and life rather than gloss over it with science, medical technology and miracle cures.

So it is not that being at spiritual home is an opportunity to be indecisive and do nothing, rather it is the source from which we can see what we do from the right perspective. It gives what we do the added bonus of being true and with good foundation. That said it is more important to get to spiritual home, than to do what we do - I think that is the main shift in approach here. Even if we do nothing if we get back to spiritual home we have lived the full life already. However we may do a very great many thing but if we never taste our own soul then we have a house without foundations.

Amazing 100BC Babbage machine!

http://www.scientificamerican.com/blog/post.cfm?id=antikythera-mechanism-an-eclipse-pr-2010-12-09

This is analogue computing!

Random Walk Again

NOTE: I must not forget that the primary purpose of this questioning is to create a realistic stock market model to test cellular automata (bots) on. Altho I realise I could just try them out on actual data and maybe that would be better. However it is intriguing to know the nature of the beast.

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Using stochastic matrix method with a matrix (M) size 21x21 following this pattern and with data from the BP (NYSE) graph i.e. p(up) = 0.47, p(same) = 0.04, p(down) = 0.49

0.04	0.47	0	0	0
0.49	0.04	0.47	0	0
0	0.49	0.04	0.47	0
0	0	0.49	0.04	0.47
0	0	0	0.49	0.04

Then after nine moves i.e. M^9 the mid row corresponding to the probability of the system arriving at any one of the 21 states starting at the middle state is (and rotated into a column):

10	0.00079792
9	0.00065137
8	0.00789282
7	0.0056751
6	0.03487872
5	0.02192446
4	0.09070506
3	0.04929454
2	0.15376394
1	0.07108634
0	0.17756573
-1	0.06818486
-2	0.14146795
-3	0.04350149
-4	0.07677832
-5	0.01780073
-6	0.02716259
-7	0.00423922
-8	0.00565518
-9	0.00044765
-10	0.00052599

Which is like the computer model I produced by brute force. But doing this again and with a different mental state myself I see that the periodicity (last post) is a natural product of the maths. As a stock market shifts state up and down the probability of it arriving at various prices is not continuous by peaked with low probability troughs between the peaks, and the dy/dx will oscillate. So like electrons around the nucleus in classical physics it will seem to accelerate between levels and then stay relatively stable inside a probability channel. Of course this is a painfully simple model of something that has an indefinable number of influences but it maybe shows the origin of the periodicity and chartist patterns that are clearly visible in the charts.

Being able to remove this random effect from stock data might reveal other things.

Thinking some more however this is probably just a sampling feature since in this model there are only 3 options. A move up, down or no move and to get anywhere in the price space is thus severely restricted making certain positions very unlikely. In reality there is a continuum of moves so these restrictions don't exist. But if higher-order patterns do exist then they may interact with each other to create oscillations. Brain-storming but worth gathering as many ideas as possible!

This also suggests a method for working out an algebraic formula for the probabilities 2do...

UK Money Supply: M4/GNP

The UK M4 money supply looks like this. Q.E. is a feature of monetary policy not some new buzz word of the recession. Obviously in a static economy if you double the amount of money in circulation then each transaction will use twice the money it did before and so the cost of everything doubles and the power of the currency halves. This is inflation.

The assumption behind increasing the money supply (Q.E.) is that the economy grows and so there are more transactions. If the economy doubled but the money stayed the same it would be the opposite of the above. Twice the transactions and so half the money would be used in each which would cause prices to halve and the power of the currency to double. This would be deflation.

Of course just having loads of cash in a bank vault doesn't make up M4. It must be in circulation which I understand is the money velocity (not being an economist - and I must stress this blog is a search for truth not an exposition of it!). The faster it moves the more transactions it can be used in and so it is more effective than money in a vault (which isn't being used as collateral against a debt that is being traded and so increases money flow by proxy obviously).

So why is inflation favoured over deflation? One argument you will hear is that an efficient pound puts pressure on other currencies so exports grind to a halt as other economies can't afford produce priced in pounds. Exports are important because they stimulate jobs, but they also stimulate the value of the currency. Take the example of the UK selling services to France. I assume this means that the French have to buy pounds on the currency markets to execute the transactions. Pound demand goes up which pushes the value higher in addition to even more transactions being executed. Imports conversely destroy local jobs and require the buyer to purchase the currency of the supplier putting the home currency into the market place and lowering its value. So to keep exports up in an economy with growing demand, the currency must be devalued by Q.E. I think this gets lost on the gold-standard fraternity.

Another argument you don't hear is that when the central bank prints money is makes money also. It buys things with the money it has printed. This is illegal for non-central banks for very obvious reasons ;-) But central banks can make money for just the cost of printing while everyone else has to do real "work" or own real "risk" to make money. I'm sure the temptation is to make a bit more than they need especially with the government pushing them to reduce the debt.

A NOTE here as I think this through: I have criticised Fractional Reserve banking before but see a bit more now. To buy a house I need some money that I haven't got. When I go to a money lender I am able to produce cash that I haven't got. The seller can actually go and get a suitcase with the £200k in it if they wish. Now in reality only a fraction of that money exists since banks lend out some 30times what they have in store, and assume that not everyone on simple probability is going to go and get a suitcase of their money at once. Pounds only represent the value in an exchange transaction not the actual value of things. The M4 is only the money in circulation not the value of the country. This is why things that aren't traded have no price - it doesn't mean they have no value! So the process of money lending is not the process of handing over the value of a house but rather entering into a complex exchange process whereby I can execute it instantly at one end and slowly at the other end through a mortgage. But the bank doesn't execute it instantly either since, in most cases, it doesn't have to produce a suitcase of cash. So it is false to think the banks are making money out of nothing by fractional reserve banking, they are simply setting up complex exchange processes that are a bit more subtle than handing things over a single counter. And anyway someone with a mortgage has just spent money they don't have and has just made money out of nothing - how else are they sitting in a house they haven't paid for yet? What this process does do is create huge inflation as argued a long time back in the blog.

Back to the point above. Rather than support inflation savers argue in favour of deflation because it means that the money they got paid yesterday is worth more today. There is less incentive to spend and so the number of transactions reduces naturally as they save which returns the value of the currency to some stable level. The built in negative-feedback device of deflation thus naturally balances that of inflation. However reducing the number of transactions reduces the amount of work in the economy which (as things are set up in current economies) will reduce the pay and so circulation of money; this might cause a downward spiral. The answer as this blog has analysed endlessly is to rethink the distribution of wealth and intelligently uncouple it from work - but that requires a re-conception of life and work (which this blog is desiring to do).

If there is a growing population then the number of transactions is going to increase naturally. With a limited money supply this will mean that less money is used in each transaction and so will lead to natural deflation. The single case where population growth leads to wealth (for a few). The deflation will lead to pressure to save, which will reduce the flow of money and cause another deflationary spiral.

There are thus very good reasons to increase the money supply to ensure that saving doesn't become too attractive. This means however that savings get hurt. To compensate, savers get an interest which is paid by borrowers. The amount that borrowers are prepared to pay depends upon their expected returns and competition between banks for lending credit. A growing economy favours lending and so interest payments. In theory the devaluation due to increase in money supply ought to be offset for savers by the increasing interest payments. However in Keynesian reality, growth is created by reducing interest payments to make credit cheap to drive borrowing and spending (the Ponzi Scheme that is the model for modern economics). Savers get little interest and then get hit by the stealth inflation in the market place, and the devaluation of their currency due to Q.E. The emphasis is on spending and debt which means we have not only today's money in our pocket but tomorrow's and the money from the day after. Massive Q.E. driving inflation. As prices go up we need to borrow more (e.g. house prices) and an inflationary spiral is entered. I imagine that eventually economist will learn to balance these forces of inflation and deflation, but at the moment, for whatever reasons, they are amateurish and incompetent.

Anyway now the point of this long foray into monetarism. The M4 money supply in the UK has increased from about £125 bill in1984 to £1400 billion in 2010. That is an increase of about 11 times. In a static economy this would result in prices increasing about 11 times. The average house price in 1984 was £75k and recently peaked at £200k so in reality an increase of only 2.6. Assuming that pressure for housing hasn't changed (not unreasonable as the population is basically the same and there has been a lot of house building in the last 26years which ought if anything to reduce prices) then house prices should have remained static which means that the economy must have expanded to take up the extra money. But still 2.6 times too much money was printed and the real economy only grew by 11.2/2.6=4.3.

A more reliable measure would be the GNP which has increased in the period from $629PPP bill to $2350PPP bill an increase of only 3.74 times. That means that 11.2/3.74=3 times too much money has been printed meaning that everything costs 3x what it should and savings are a 1/3 less powerful then they should be! This agrees with the rough measure above and supports the assumption that pressure for housing hasn't actually increased. The economy has actually only increased by a factor of 3.74 instead of 11.2 while the pound has actually weakened to a third and prices are 3 times what they were. That was the basis of the "apparent" booms that Brown and others have resided over.

So now back to stock markets. If you invested £1000 in the stock market in 1984 with economic growth of 3.74 it should be worth £3740 today (assuming your companies expand in accordance with the general economic growth). However M4 money printing has been going on. If it was in line with the 3.74 growth then the pound would remain stable and you would have £3640 today. But we know that 11.2 times as much has been printed (3 times too much) so actually the buying power of the pound has reduced to a 1/3. So the £3740 we see on the balance sheet is really only worth 1247 (in 1984 pounds). That is an actual increase of 125% in 26 years that is just 0.86% per year. Put that another way we need to make 26root(3)= 4.3% a year to keep up with the excessive money printing.

The relevance of this to the stock modelling is that an upward trend of 4.3% a year is present not because of anything in the stock market but because of the devaluation of the currency. This is maybe enough to turn a lot of down moves into up moves and bias what is perhaps a random pattern. Removing this up-trend might also make modelling the distributions easier. A new dataset removing the M4/GNP data is required.

Here is data from http://www.marketoracle.co.uk/Article24619.html

Since 1987 the value of the pound based on the RPI has dropped to 44%. Extrapolate backwards to 1984 and that is 35% similar to the 33% above.

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Here is the UK treasury data on GDP and also inflation.

http://www.hm-treasury.gov.uk/data_gdp_fig.htm

£100 in 2009 is the equivalent of £42 in 1984. That is substantially higher than the 33% above but will do to begin with.

Stock Direction Correlation & Distance Correlation

Comparing Up/Down movements of successive days in the FTSE gives us this unexpected result. Given today's close relative to yesterdays as Up/Down what what the previous move?

Yesterday was Down: Today was:

Up 1673 25.0% 52.5%

Down 1513 22.6% 47.5%

Total 3168 (of total) (of down)

Yesterday was Up: Today was:

Down 1673 25.0% 47.6%

Up 1839 27.5% 52.4%

Total 3512 (of total) (of up)

There are only 18 days when the two days close the same i.e. 0.3% so I'm ignoring this event.

I don't need to do stats on this: there are 6698 events! and unbelievably the Up/Down and Down/Up counts are the same really suggesting that it makes no difference whether yesterday was an up or a down to signal a change in direction: it happens 25% of the time i.e. the Expected value based upon a random assumption.

However if yesterday was Up then there is a more than average chance that today will be up also! 27.5%.

Conversely if yesterday was down there is a less than average chance that tomorrow will be down!

In the stock walk then, the stock has a 52% chance of going up again and 48% chance of falling. Does this explain the trend of the stock market up or is distance a feature also, that is, are moves down bigger than moves up or vice versa.

The total log distance moved in the period is from 7.010402 on the 4th Feb 1984 to 8.642715 on 26th Nov 2010 which is +1.63231. There are 3522 up events (52.4%) in total and 3194 down events (47.6%) i.e. an excess of 328 up events to account for the up shift, if up and down are the same size. So we would expect each event to be on average a shift of 0.5%.

We can calculate that exactly from the data. The average move irrespective of direction is 0.7922% much bigger. This breaks down to:

Average move Up is: 0.7805% against an average move down of -0.81%.

So to summarise the probability of up moves is 10.3% more likely than down moves, but the size of down moves is 3.7% larger than up events. The average daily swing is also larger at 0.8% than the minimum expected at random of 0.5%.

A Model

N = number days -1. Pu/Pd is probability of up/dow

n. Du/Dd is average distance up/down.

Total distance Up = N.Pu.Du

Total distance Down = N.Pd.Dd = N.(1-Pu).Dd

Net distance D = Total distance Up - Total distance Down = N [Pu.(Du+Dd) - Dd)]

Our data set has N=6735 interday events. Pu = 0.524. Du = 0.0078. Dd= 0.0081

D = 1.56

Data for BP dataset.

Yesterday was Down. Today is:

Up 1640 25.5

Down 1486 23.1

Yesterday was Up. Today is:

Down 1585 24.7

Up 1717 26.7

There are 4.5% events when the stock closed the same. Probably a feature of the lower stock value and therefore less significant figures and then rounding errors. Ignored.

There is a similar pattern to the FTSE. Noticeably the probability of an Up is higher if yesterday was a Down than the other way around. I need to think about this in relation to the extraordinary result from the FTSE.

Average distance Up is: 0.012396

Average distance Down is: -0.0124

Total average distance: 0.011868 (including days when stock same)

Interestingly unlike the FTSE the average moves up and down are the same. This means the trend over time is because of the probability of up/down rather than the size!!! Very interesting from a trading point of view!! (Maybe individual stocks work like this while the FTSE is a conglomeration of different sectors each with different performances each day and so has changing behaviour.)

The Model is a bit simpler here:

N = 6428, Pu = 0.514, Du = 0.012

D = N [Du(2.Pu - 1)] = 2.16 (Actual value of : 2.28)

Next up is there a correlation between distances?

Not Obviously but stats tests show otherwise. A two tailed on the complete data of today's price change against tomorrow's was less conclusive with the Pearson not even being significant.

Correlations
		Today	Tomorrow
Today	Pearson Correlation	1	.008
	Sig. (2-tailed)		.534
	Sum of Squares and Cross-products	1.927	.015
	Covariance	.000	.000
	N	6733	6733

The Spearman and Kendal-tau measures show a significant correlation between todays and tomorrows stock moves.

Correlations
			Today	Tomorrow
Kendall's tau_b	Today	Correlation Coefficient	1.000	.022**
		Sig. (2-tailed)	.	.008
		N	6733	6733
	Tomorrow	Correlation Coefficient	.022**	1.000
		Sig. (2-tailed)	.008	.
		N	6733	6733
Spearman's rho	Today	Correlation Coefficient	1.000	.031*
		Sig. (2-tailed)	.	.010
		N	6733	6733
	Tomorrow	Correlation Coefficient	.031*	1.000
		Sig. (2-tailed)	.010	.
		N	6733	6733
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed). However taking absolute values and so only looking at the size of the change the correlations are not surprisingly extremely significant. Today_pos Tomorrow_pos Today_pos Pearson Correlation 1 .210** Sig. (1-tailed) .000 Sum of Squares and Cross-products .979 .205 Covariance .000 .000 N 6733 6733 Correlations Today_pos Tomorrow_pos Kendall's tau_b Today_pos Correlation Coefficient 1.000 .067** Sig. (1-tailed) . .000 N 6733 6733 Tomorrow_pos Correlation Coefficient .067** 1.000 Sig. (1-tailed) .000 . N 6733 6733 Spearman's rho Today_pos Correlation Coefficient 1.000 .101** Sig. (1-tailed) . .000 N 6733 6733 Tomorrow_pos Correlation Coefficient .101** 1.000 Sig. (1-tailed) .000 . N 6733 6733 **. Correlation is significant at the 0.01 level (1-tailed). I'm assuming 1-tailed because values are only positive. This comes as little surprise however because we would expect big moves to be followed by big moves. A technical ought to be available then (maybe Bollinger) which determines the size of moves to expect. Then rough trend to confirm this belief by linear regression is: Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) .009 .000 46.520 .000 Today_pos .210 .012 .210 17.586 .000 a. Dependent Variable: Tomorrow_pos Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) .009 .000 46.520 .000 Today_pos .210 .012 .210 17.586 .000 a. Dependent Variable: Tomorrow_pos So indeed the size of tomorrows price move is a positive function of todays price move (significantly). [Stats courtesy of SPSS.] Summary

to be summarised and expanded...

===

Adjusting the figures for inflation (which approximated to GNP/M4) the distribution of up/down was only slightly affected.

Yesterday was Up. Today was:

Up 26.9%

Down 25.0%

Yesterday was Down. Today was:

Up 25.0%

Down 23.0%

Total Up=52% versus down=48% so same as before.

Removing the upward bias hasn't changed many of the ups into down but it seems to have operated selectively. It has either turned UUs into UDs or DUs into DDs or taken UUs and made them DD (less likely). Suggesting that these were weak relationships.

For the BP data the effect is more obvious with only UU standing out as a feature of the data now.

UU 26.5%

UD 24.5%

DU 24.6%

DD 24.3%

Correlations
		VAR00001	VAR00002
VAR00001	Pearson Correlation	1	.210**
	Sig. (1-tailed)		.000
	N	6733	6733
VAR00002	Pearson Correlation	.210**	1
	Sig. (1-tailed)	.000
	N	6733	6733
**. Correlation is significant at the 0.01 level (1-tailed).

Correlations
			VAR00001	VAR00002
Kendall's tau_b	VAR00001	Correlation Coefficient	1.000	.067**
		Sig. (1-tailed)	.	.000
		N	6733	6733
	VAR00002	Correlation Coefficient	.067**	1.000
		Sig. (1-tailed)	.000	.
		N	6733	6733
Spearman's rho	VAR00001	Correlation Coefficient	1.000	.100**
		Sig. (1-tailed)	.	.000
		N	6733	6733
	VAR00002	Correlation Coefficient	.100**	1.000
		Sig. (1-tailed)	.000	.
		N	6733	6733
**. Correlation is significant at the 0.01 level (1-tailed).

OK the trends are still there after removing inflation.