Astrology? Tea leaves? Augering? ( flight of birds) Gips

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Financial Time Series

• Dave Elliman

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For Example Tesco
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What can we deduce

• The price declined from May to August and then
  recovered?
• The volume tends to be higher when price changes
  are faster?
• Tesco will go up a lot further?
• Tesco is very volatile?

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What can we know?

• Things in the past
• The future is unknown. If you know how to
  predict the future please see me afterwards
• The average returns in the past have been µ per
  year. Call this the expected return but over
  what period?
• The price jumps about a lot, recently the
  standard deviation has been s. over what
  period?

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What Finance Theory Assumes

• That returns have a mean level (the expected
  return) and if that is removed, what is left are
  random fluctuations drawn from a normal
  distribution.
• The standard deviation of the random variation is
  reasonably stable in time.
• In other words
• Trend return discount rate risk
• You cant predict the price tomorrow from
  historic information
• The future looks a lot like the past

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Is any of this true?

• In stable periods to a first approximation it
  seems close
• The distribution is not normal (see todays
  worksheet)
• The volatility is not stable with time but occurs
  in bursts
• The future is not like the past at the moment!
• Dont expect figures from the real world to fit
  financial formulae too closely!

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Predicting the future

• déjà vu Advice to a young boy
• Good guess Advice toTerri
• Astrology?
• Tea leaves?
• Augering? (flight of birds)
• Gipsy Rose Lee
• Technical analysis or Chartism

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Tasseographers, astrologers?
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The art of Tasseography (reading tea-leaves)
This means I am overdue for some happiness with
a woman.
I am about to make a fortune by means of
foresight about going downwards as a result of my
knowledge and learning. However there are some
obstacles ahead.
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The art or science of Technical Analysis
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Technical Analysis
http//www.investopedia.com/university/technical/t
echanalysis8.asp
Any truth in this?
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Are there patterns in the stock market?
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The Head and Shoulders
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The Cup and Handle
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The Double Bottom
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Is this a head and Shoulders Pattern?
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Is this a Double Bottom?
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Pareidolia I
A face in the snow?
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Pareidolia II
A face in the clouds?
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Human psychological traitsApophenia
Confabulation

• Apophenia Seeing signs and symbols
• charged with significance in random or
• meaningless data.

eg The DaVinci Code!
Confabulation A plausible but imagined memory or
explanation that fills in gaps in what is
understood and remembered
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Confabulation?

• The FTSE 100 closed above the psychologically
  important 5,000 mark, boosted by strong gains on
  Wall Street amid relief that a report showing a
  slowdown in manufacturing growth in May was not
  as grim as some had feared, dealers said.
• London shares were higher in early deals as
  strong gains in drinks giant SABMiller added to
  positive earnings news overnight from US
  bellwether IBM, dealers said.
• Meanwhile, in New York shares ended lower, with
  the Nasdaq and the SP 500 snapping a
  seven-session winning streak, after
  weaker-than-expected earnings from Citigroup
  prompted some investors to cash in on recent
  gains.

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A Pattern is

• A member for a known set of categories
• A set of relationships between parts
• An emergent property of a system
• A property of a system that allow its description
  to be shortened

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The FTSE 100 since 84 Again
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Daily Returns are more convenient
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The Conventional View

• A Random Walk with normally distributed step size
• For the FTSE 100
• Average 3.54x 10-4
• Standard Deviation 1.028 x 10-2

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Do the simulated and actual returns look alike?
Could it be that established financial theory is
built on dubious assumptions?
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Are there Harmonic Components?
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Is there Momentum
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The Kalman Filter is a Disappointment
The mean is very close to zero
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Perhaps the EMH is right? BUT.

• Remember the connection between patterns and
  compression?
• If it is a random walk we would expect about the
  same compressibility

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Can we compress the series?

• Represent as 1 one for ve return 0 for ve
  (drift removed)
• Compare with random series
• Use Markov arithmetic coder

YES! The real series is somewhat more
compressible lt 1 effect but consistently so over
30 years
These compression algorithms use quite a small
window So this is a short term effect
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My lossy compression
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My lossy compression
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My lossy compression
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My lossy compression
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Keep splitting until max error lt T

• Represent a line as (?x, ?y)
• Are there less lines in a real series as opposed
  to a random one?
• Answer Yes! (about 3 to 5 less)
• Can we compress the real series more than a
  random one? (are the values of ?x and ?y less
  random than chance?)
• Answer Yes! (about 8 mode compression possible)

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We need a Trading Strategy
Any ideas?
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Sornettes Compression! (S P 500)
Nearly 3 years
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We could try simulation.
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The Assumptions are not Realistic

• Traders do not seek to be in the minority
• Traders are seeking profit so we use
• 4 Predictions Top Bottom Up -
  Down
• 3 States Long - Short Cash
• Scale-free influence network
• Influence increases with Volatility

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But the Complexity of this new model is a big
disadvantage.
Octave Levenspiel says Give me four parameters
and I will model and elephant.
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Can we synchronise our model to real market data?
Yes! It works some of the time.
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The model predicts direction, and is more often
right than wrong
Take the best 10 of days and the model gives
odds of 5545 in your favour
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The model is only a first prototype

• Others build a set of models and choose the best
• The feedback mechanism needs to be much improved.
  We are working on using an Ensemble Kalman Filter
  to achieve this
• It may be useful to add a market-maker to give
  greater liquidity.

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Conclusions

• Markets sometime have a (perhaps small)
  deterministic component
• Our model seems to capture some part of the
  internal market state
• Prices move fastest when there is evidence of
  herding
• There are many ways in which our model could be
  improved

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Can market be predicted?
What would happen if a successful pattern were
found?
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What If a successful model was adopted?

• The odds would be changed in favour of those who
  used it
• The market would change and models would have to
  take account of the model and so on forever
• An arms race!

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People see patterns everywhere But

• What would happen if such patterns were
  predictive and a significant volume of trading
  followed them?

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The AutoCorrelation Function
Is a time series correlated with itself over some
time lag? Are there seasonal effects? Is the
advice Sell in May and go away! correct? Do
equities tend to rise on a Tuesday? You should
pick up a small ex-dividend effect What is the
autocorrelation function of a random walk?
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Things to try

• Is there any periodicity? Try an auto-correlation
• Is there any dependence with a time lag?
  Cross-correlation
• SOX (Philadelphia) ? ARM.L made me some money!

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Autocorrelation Function for White Noise
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Calculating the Autocorrelation Function

• You can put the formula into Maple directly, but
  there is a faster way.
• The autocorrelation function is the same as the
  Fourier Transform of the Power Specrum. This may
  be worthwhile if the calculation is slow.

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Any Questions?