A simple 'auto' trader was designed to interpret th

1
"Predicting randomness experiment new
perspectives and results from the test run

• Nikita Stepanov, ITEP/CERN/GRC, 19.05.2004

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Outlook

• Introduction (what is it? And why? And how?)
• Status (hardware and software)
• Data sources (description, random properties)
• Selected results from the test run
• More (more practical results)
• Conclusion (new goals and perspectives)

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Predicting randomness experiment. Motivations,
primary goals etc
Predicting randomness experiment was proposed
about one year ago with the purpose of
investigating the randomness of bit sequences
generated by different random sources so as to
elucidate if such sequences may be locally
predictable in statistically significant sense by
the human being or intelligent computer
program. The experiment was designed to be the
large scale internet initiative (game) which
could allow thousands of participants around the
world to be involved. Why game? The technical
approach we proposed can be considered a formal
analogy with a game involving many players
versus a fair market. Any player observes the
past data represented as a 1D discrete RW. At any
step the player is allowed to bet on the
direction of the future RW trajectory
continuation or, according to the real market
game terminology, to open UP or Down
position. He (she) is able to close the open
position in any time in future obtaining the
profit/loss equals to the number of steps the
RW makes in the predicted direction minus the
number of steps in opposite direction.
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Predicting randomness experiment. Motivations,
primary goals etc

• Finally, the prediction ability of a given
  experiment participant can be quantified
• by analyzing the whole sequence of
  profit/losses generated by him.
• This approach closely resembles the real market
  game (in the no transaction
• costs regime) and allows us to use the
  commercial trading system (kindly
• provided by Dukascopy Trading Technologies
  Corporation (Dukascopy) as a
• basis for our experiment. This analogy also
  motivates the nick name for the
• experiment adopted at the time of proposal Deep
  Trader
• See for details the paper Predicting
  randomness available at
• http//grc.dukascopy.org/
• Primary goals
• To test experimentally the validity of the
  efficient market hypothesis
• To investigate the behavior patterns of human
  brain when making
• the trading decisions
• 3) (the ultimate goal) to detect and quantify
  some anomalous human brain ability to predict
  the future for the truly random processes.

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Present status software
Data sources
Remote Client (Java applet)
Java server
Data processor
Data processor

• Stress tests indicate that a single Java server
  can serve up to 700 1000 client applications
  simultaneously.
• The system is easily clusterizable
• A special instance of Java server is
  instantiated to serve the experiment needs

Central Oracle DB
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Present status hardware

• The central computing facility is a scalable
  multilevel cluster.
• At present the system comprises 28 CPUs with
  total operative memory of 30 GB
• and 1 TB of HDD space, and it services
  approximately 8 million requests daily.

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Data sources (bit sequence generators)

• Design constraints
• 1) standard simple data representation
  (analysis)
• 2) psychologically pleasant update frequency
• Each data source generates 1/-1 signal every
• 10 sec
• The resulting sequence of bits is represented as
  an integer valued RW (next value old value
  new generated bit) to allow the standard
  graphical representation and technical analysis

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EURRAND
Bit source driven by the market EUR/USD quote
according to the following simple algorithm
Candle 10 sec aggregation of the EUR/USD stock
tick data It has opening, closing, high, low
prices Diff candle.closingPrice(T)
candle.closingPrice(T-10 sec) If (Diff gt 0)
newBit 1 else if (Diff lt 0) newBit
-1 else newBit pseudoRandom.getBit()
Note the sequence becomes pseudo
random on weekends, otherwise, it more or
less mimics the behavior of EUR/USD
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GEIGER

• The Geiger counter (standard RM-60 device by
  AWARE Electronics
• Company http//www.aw-el.com ) registers
  natural radioactive
• background with average count frequency about 8
  counts/10 sec.
• It is connected via serial port to the PC, where
  a simple program
• supports a 10 sec. time interval slots b)
  registers any counter signal
• appearance with accuracy around 0.1 msec and c)
  generates 1 / -1 bits
• according to the following algorithm
• At the end of each 10 sec time slot (last 9999-th
  msec.), the program
• checks first whether at least one signal is
  registered during the current
• 10 sec slot. If yes, then it takes the
  millisecond of arrival of the last
• signal and generates 1 if this msec. is even and
  -1 otherwise.
• In (rare) case when there are no signals during
  this 10 sec slot, the
• program generates a pseudorandom bit.

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PSEUDO RANDOM

• Matsumotos twisted generalized shift register
  generator TT800 as described in his article
  published in ACM Transactions on Modeling and
  Computer Simulation, Vol. 4, 3, 1994, pp.
  254-256.  Our C implementation is based on the
  C code by M. Matsumoto. 
• CA (Rule 30) pseudo random generator patented by
  S.Wolfram (thanks to his kindly permission).
  Despite the very simple and deterministic
  evolution rule, this CA random generator
  systematically passes new more and more
  sophisticated statistical tests. (see, i.e. S.
  Wolfram A new kind of science, Wolfram Media,
  Inc, 2002)

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Testing random source properties statistical
test
In the statistical approach the randomness is
treated as a probabilistic property. Any
statistical test is formulated to test the
hypothesis (H0) that the sequence being tested
is random. To construct the new test, one needs
to 1) select a certain property of truly
random sequence 2) estimate the relevant
statistics, i.e. the distribution of the possible
outcomes of the test under the assumption of
randomness 3) fix a certain significance level a
(typically 0.01 or 0.001) to accept/reject H0.
For a given generated sequence the statistical
test calculates a certain P-value, which can be
interpreted as a probability that a truly
random sequence will produce the result which is
less random then the sequence being
tested. Say, P(s) lt a 0.01 indicates that
about 1 truly random sequence out of 100
will be rejected by this test, thus the test
outcome P(s) gt 0.01 allows one to accept a given
sequence as random at 99 confidence level.
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statistical test simplest common example
Frequency (Monobit) test
The purpose of the test is to determine
whether the number of 1 and -1 in a sequence are
approximately the same as would be expected for a
truly random sequence. Test variable S
abs( S Si) / sqrt(N), where Si is the I-th bit
and N is the total length. The distribution
S/sqrt(2) has to be half-normal, therefore,
P(S) erfc(S/sqrt(2)) where erfc is a
complementary error function P(S) lt 0.01
rejects H0 at 99 confidence level
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The battery of statistical tests

• Problem there are an infinite number of possible
  tests.
• No specific finite set of tests is deemed
  complete.
• Negative example the binary extension of p
  passes all
• known statistical tests.
• The practical recipes 1) use the massive and
  representative battery of statistical test to
  estimate the
• random properties. 2) keep in mind that
  results have to
• be interpreted with a certain grain of
  salt.
• Useful ref. http//csrc.nist.gov/rng/ (Nist
  Statistical Test
• Suite explained)

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The battery constructed

• Frequency (monobit) test
• 4 Block frequency tests for the block sizes 4, 8,
  16, 32
• Runs test
• 4 Longest run tests for the block sizes 8, 128,
  512, 1000
• 50 Non overlapping template matching tests for
  the different bit patterns
• 12 Serial test for the template length 3-14 (each
  test includes in fact 2
• different tests)
• 12 Approximate entropy tests for the template
  length 2-13
• Random excursions variant test (includes indeed
  18 tests for
• the different RW states from -9 to 9)
• 85 (114) stat tests in total, aimed to detect
  the absence of
• short term correlations in bit sequence

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Battery applied

• EURRAND passes 33 (0.338) fails 52 (0.612)
• GEIGER passes 39 (0.459) fails 46 (0.541)
• PSEUDO 1 passes 85 (1.000)
• PSEUDO 2 passes 84.5 (0.994) fails 0.5 (0.006)
• (fails one of two tests included in the serial
  test for the template length 14)
• Q? Why GEIGER is so regular?

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Selected results and lessons from the test run

• Final rules of the game
• 1) Each participant initially receives the
  starting capital of 10000 units 2) He is
  allowed to open just one 1 lot position on
  every stock simultaneously one step reward is
  /- 1 unit. 3) 3 stocks are available EURRAND,
  GEIGER and PSEUDO. The trading results for each
  stock are analyzed separately.
• Main lesson EURRAND and GEIGER stocks are indeed
  predictable both by human and AI predictors. It
  is, however, the tantalizing exercise for a
  human being to demonstrate the statistically
  significant performance many noisy deals,
  dropped bad portfolios, lengthy learning
  period, etc (like in the live trading). It seems
  to be that the main obstacle is the human
  psychology. Every successful run appears to be
  quite hard and concentrated work for several
  weeks.

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Selected results and lessons from the test run

• It looks almost meaningless to analyze the human
  predictions statistics as a whole. The data are
  too noisy and spoiled by the lazy and
  frustrated participants. It is more appropriate
  to concentrate on the analysis of the results of
  an every single participant.
• AI predictors easily outperform human ones on
  the predictable stocks EURRAN and GEIGER. The
  results for the PSEUDO stock are less apparent
  all tested AI predictors failed definitely, as
  there are no (almost no) local correlations to
  exploit. At the same time, some obstinate
  humans stubbornly kept staying at significance
  level of about 1 1.5 for a long trading
  period. We can not report any positive results,
  but . perhaps, there is something funny!

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Main practical result

• EURRAN stock seems to be easily predictable.
  Does it mean that the efficient market hypothesis
  is not valid? Directly not,
• because EURRAN is just the surrogate stock,
  derived from the real EUR/USD. During the last
  year we have made a lot of other investigations
  trying to answer this question and now we can
  definitely answer yes, it is not valid. Indeed,
  the market data are locally correlated and
  contain the exploitable patterns.
• We are definitely not alone and not the
  first ones. There is a plenty of publications on
  this subject. We have just provided the practical
  evidence in order to convince ourselves and now
  we are trying to answer yet another practical
  question is there enough predictability to beat
  the market in live trading?

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Performance estimators

• Simple robust estimator valid for the large
  number of predictions
• Signif E(p) /
  sqrt(D(p)/N )
• where E(p) average profit, D(p)
  profit dispersion.
• More descriptive estimator based on subsequence
  selection (proposed by A.Duka) Let S be a bit
  sequence. For a given predictor P 1) Select all
  segments of S which corresponds to P positions
  history of P (each position (prediction) has
  starting time and closing time) 2) In each
  segment multiply all bits by the prediction
  direction (1 or -1) 3) Construct new
  subsequence SP from selected segments and
  represent as 1D RW. Then the deviation R0 of the
  RW end point from 0 may be the measure of the
  predictor performance. As a quantitative
  predictor performance estimate, one can use,
  i.e., the probability that the end point of the
  realization of true RW of the same length N
  will has the deviation R which is equal or above
  R0. For large N next approximation is valid
• P(R gt R0) ½
  erfc(R0/sqrt(2N))

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Most obstinate human predictor

• Nick name forecast
• Active period 7.11.2003 16.11.2003 (9 days of
  hard work!)
• Number of positions (predictions) 1120 (610
  down, 510 up)
• Total profit 414 average 0.37 Significance
  2.85
• Average position length 20 steps
• Effective length 22400 steps P(R gt 414)
  0.00279
• General comments the learning phase roughly
  takes one have of the total run the statistics
  for the second half looks significantly better (
  1-st half ltPgt 0.23 2-nd 0.45) the
  performance is not stable locally, one can see
  some periods of frustration.

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AI predictors recurrent neural network
Recurrent NN
Feed forward NN
Output layer
Input layer
Major difference RNNs often exhibit very reach
dynamics. FNN just maps the input to the output,
RNN can run forever being triggered once by a
single input signal. RNNs were found especially
suitable for the time series prediction, because
they can generate some sort of long term memory.
The price is indeed high BackProp is still
applicable, but has to be run formally forever
for a single input because of the feedback
connections.
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RNN implementation details
Particular RNN architecture used for all
prediction tests Single input node, 6 hidden
nodes (fully connected), one output node (6 6
6 36 1 1 56 real parameters) Activation
function symmetric sigmoid. RNN was trained to
predict next bit. A simple auto trader was
designed to interpret the recommendations of
RNN predictor in order to make results comparable
with those of other (human) predictors. Train
sequence 3000 bits Test sequence (next) 3000
bits 10 different runs for randomly chosen 6000
bits subsequences for each data source (for the
EURRAN the weekends are excluded)
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RNN performance EURRAN
Generation 50 Performance on the training
set Number of deals 1672 Total profit 580
Number of UP deals 835 Number of DOWN
837 Average profit/deal 0.347 std 1.085
Significance 13.07 Total active length 2998
Average position length 1.793 Performance on
the validation set Number of deals 1670
Total profit 596 Number of UP deals 834
Number of DOWN 836 Average profit/deal 0.357
std 1.032 Significance 14.14 Total active
length 2998 Average position length 1.795 P(R
gt 596) lt 10(-27)
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RNN performance GEIGER
Generation 150 Performance on the training
set Number of deals 1097 Total profit 436
Number of UP deals 548 Number of DOWN
549 Average profit/deal 0.397 std 1.940
Significance 6.79 Total active length 2996
Average position length 2.731 Performance on
the validation set Number of deals 1129
Total profit 358 Number of UP deals 564
Number of DOWN 565 Average profit/deal 0.317
std 1.763 Significance 6.04 Total active
length 2998 Average position length 2.655 P(R
gt 358) 1.42 10(-9)
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RNN performance PSEUDO RANDOM
Nothing was captured in 1000 generations!
Performance oscillates around 0. Results for 350
generations Performance on the training
set Number of deals 1614 Total profit 338
Average profit/deal 0.209 std 1.400
Significance 6.01 Total active length 2998
Average position length 1.858 Performance on
the validation set Number of deals 1639
Total profit 9 Average profit/deal 0.005 std
1.319 Significance 0.167 Total active length
2995 Average position length 1.827
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Human being and RNN similarity and difference

• RNN definitely outperforms the human predictors
  on the simple predictable sequences. The
  trading strategies are quite different the
  average position length for RNN predictor is
  about a factor of 10 shorter, also, the
  profit/loss fluctuations are much high for a
  human predictor. It seems to be, that it is
  psychologically difficult for the human being to
  change (reverse) his (here) prediction opinion.
  Does it means that the human psychology is always
  playing against the trader?
• The asymptotic performance is indeed rather
  similar it looks like both type of predictors
  can be learned to exploit almost all useful
  regularities in the sequence generated by the
  GEIGER source. Average RNN profit/prediction
  0.31 Human 0.25 0.37
• Computational complexity RNN complexity is
  perfectly controllable. The complexity of the
  human brain is of course much high, however, it
  does not mean that the part of the brain computer
  allocated for the particular prediction task has
  much high complexity than RNN predictor.
• The intriguing question arises Are the
  computational complexities of these predictors
  comparable?

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Towards the practice real market game in zero
transaction cost (ZTC) regime

• Weak efficient market hypothesis (WEMH)
• Technical analysis is useless.
• Famous G.P. Morgan prediction Prices will
  fluctuate.
• Technical analysis any approach using just
  the information available from the time series
  itself. It can be quite sophisticated different
  data representations (candles, PF, Fourier
  transforms, wavelets, etc) technical indicators
  patterns, correlation analysis etc but no
  fundamental analysis.
• Any predictor trying to deduce the future
  behavior from the known past has to generate the
  asymptotically zero-sum game being applied to the
  real market even in ZTC regime. Is it so
  hopeless?
• It can be shown easily that indeed WEMH is
  wrong.

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A.Duka test portfolio
100 trading days 768 deals (7.7 daily) Average
profit 130.24 Std 761.2 Sharpe ratio
0.171 Significance 4.74 Varity of stocks Varity
of different strategies. See for
details http//www.dukascopy.com
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AITraders

• Keeping in mind the evident success of machine
  predictors applied to the trading on the
  artificial stocks, one can think about more
  practical applications to the real market.
• There is a plenty of the modern promising AI
  techniques.
• The basic postulate (quite questionable
  indeed) any detected pattern can be exploitable
  for some short period in future then it will
  disappear or even reverse to its negation.
• My particular favorites are adaptive multi
  agent systems. The basic ingredients of the
  cooking evolutionary incremental learning
  (almost) zero number of hardwired parameters
  easy transition from the majority to minority
  easy forgiveness of the past successes soft
  implementation of the expert knowledge
  inhomogeneous agent committee

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AITraders

• Keeping in mind the comparable success of machine
  predictors applied to the trading on the
  artificial stocks, one can think about more
  practical applications to the real market.
• There is a plenty of the modern promising AI
  techniques.
• The basic postulate (quite questionable
  indeed) any detected pattern can be exploitable
  for some short period in future then it will
  disappear or even reverse to its negation.
• My particular favorites are adaptive multi
  agent systems. The key ingredients of the
  cooking evolutionary incremental learning
  (almost) zero number of hardwired parameters
  easy transition from the majority to minority
  easy forgiveness of the past success soft
  implementation of the expert knowledge.

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AITraders ZTC example 1
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AITraders ZTC example 2
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From ZTC to real life is it possible to beat the
real market on the systematic basis?

• In ZTC regime everything looks perfect.
• Does it means that the market is beatable in the
  real life, i.e. when the realistic transaction
  cost is taken into account? Many strategies
  become losers now or at least demonstrate rather
  modest performance. It is especially true for the
  aggressive scalping strategies trying to
  exploit short term correlations.
• But is it completely hopeless?

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Dukascopy trading contest
(alternative Hard Predicting Randomness
experiment?)
Runs since October, 2003 on the monthly
basis Already involves about 1200 participants
(150 monthly) Competition rules are simple
Each trader receives (the virtual) 50000
capital and tries to beat the real market in CFD
trading. The trader with the largest final
balance wins the monthly competition cycle. The
trading conditions are identical to those for the
live trading (spreads, commissions, margins etc)
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Dukascopy trading contest statistics is
available now
Already after a brief analysis of the contests
statistics one gets a very strong impression that
a certain quite stable subgroup (say, about 10)
demonstrates amazing performance (i.e. prediction
ability) Recently Dukascopy kindly opens the
access to the (non private) part of the
competition statistics for the scientific
analysis
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Dukascopy trading contest April results
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Dukascopy trading contest March results
About 600 Positions!!!
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AITraders in real regime example 1
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AITraders in real regime example 2
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Summary -1-

• We are ready to conduct experiment in full scale.
  The starting date is today. We are planning 1
  year of running.
• For those who wants to play against the
  artificial market,
• the registration procedure is similar to the
  standard registration of the demo/live account
• 0) enter the Dukascopy web page
• 1) Fill the Dukascopy live trading
  registration form,
• typing experiment instead of bank
  attributes
• 2) You will receive the login/password to
  access the deal station
• 3) To launch the deal station follow the link
  CFD client entry from the main Dukascopy page
  type your login/password in the proper fields
  then push the button Enter DDS
• Thats it. You will be allowed to trade
  just the artificial quotes located in the special
  quote folder physics. Your trade will be
  commissions free and subjected to the rules
  accepted for the experiment.

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Summary -2-

• Grand prize 5000 to the live Dukascopy
  trading account
• (one can be withdraw without any live
  trading )
• Future winner experiment participant which
  will demonstrate the best performance predicting
  the most difficult PSEUDO market.
• Necessary conditions
• 1) Result has to be demonstrated in the
  real-time regime
• 2) At least 1000 predictions (positions)
• 3) Statistical significance gt 3
• Decision date 1 June 2005

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Summary -3-

• GRC is proposing new research initiative
• the main goal is the development of the
  next generation trading/analysis software Smart
  trader machine (STM) which will help trader to
  survive in modern hostile market environment
• The main design patterns
• STM will be designed in such a way, that
  any useful pattern, approach, algorithm etc can
  be easily incorporated. Most likely STM will be
  able also to develop its own new knowledge and
  algorithms and support as well advising and auto
  trading regimes. Another desirable (and, in
  principle, realizable) feature of this new
  software may be the possibility to learn and
  adopt to any concrete human trader stile.
  
• GRC opens the research grand program for the next
  year (2005) to support this new initiative. Any
  (reasonable) and motivated approaches are welcome.

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Very last comment

• For the developers of new smart trading systems
• Dukascopy has presented recently two new
  services
• 1) Customized data feed which allows one to
  integrate into his application a reliable source
  of real-time and historical data.
• 2) Auto execution service providing the
  execution of trading orders (in demo regime)
  generated from user application.
• Both are realized using MSFT Web Service
  technology, which allows one straightforward
  integration in virtually any programming
  language.
• Both services are free of charge for GRC
  participants