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Data Mining Methods on Time Price Series for Algorithmic Trading Systems

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Abstract and Figures

Buy cheap and sell more expensive. This is the main principle to make a profit on capital markets for hundreds of years. The rule is simple but to apply it in practice has become a very difficult task nowadays, with very high price volatility in the financial markets. Once electronic trading was widespread released, reliable solutions can be found using algorithmic trading systems. This paper presents a data mining method applied to the time price series in order to generate buy and sell decisions using computational algorithms. It was found that an original data mining method based on the price cyclicality function gives us an important profit edge when it is about the capital investments on the short and medium term. The Cyclical Trading Method will be presented together with the main principles and practices to design and optimize trading software. Test results are also included in this article in order to compare the presented method with other known methodologies to trade the capital markets.
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26 Informatica Economică vol. 23, no. 1/2019
DOI: 10.12948/issn14531305/23.1.2019.03
Data Mining Methods on Time Price Series
for Algorithmic Trading Systems
Cristian PĂUNA
Economic Informatics Doctoral School
Bucharest Unversity of Economic Studies
cristian.pauna@ie.ase.ro
Buy cheap and sell more expensive. This is the main principle to make a profit on capital
markets for hundreds of years. The rule is simple but to apply it in practice has become a very
difficult task nowadays, with very high price volatility in the financial markets. Once electronic
trading was widespread released, reliable solutions can be found using algorithmic trading
systems. This paper presents a data mining method applied to the time price series in order to
generate buy and sell decisions using computational algorithms. It was found that an original
data mining method based on the price cyclicality function gives us an important profit edge
when it is about the capital investments on the short and medium term. The Cyclical Trading
Method will be presented together with the main principles and practices to design and optimize
trading software. Test results are also included in this article in order to compare the presented
method with other known methodologies to trade the capital markets.
Keywords: Data mining, Time price series, Capital markets, Cyclical trading method, Trading
algorithms, Trading software
Introduction
The main condition to make a profit on the
capital markets is to buy cheap and to sell
more expensive. This simple principle was
explained even in the oldest book about
trading. In the year of 1688 José de la Vega
present this rule in the Confusion de
Confusiones” [1] together with other two very
important aspects regarding the financial
investments: the unpredictability of the stock
price evolution and how important is to have
patience in order to make the profit. Even
from the beginning, the investors knew that
they can lose money and they have to be
patient in order to recover and to make a
profit. After more than three hundred years
nothing was changed about these simple truths
of the capital investments.
Even the basic principles remain the same, the
tools and methods we are using today to
manage the price evolution and to build the
trading decisions are different. The electronic
trading systems globally implemented in all
stock exchanges in the world permit us today
to have fast access to the price evolution, to
analyze the price behavior in real time, to
build almost instantly the trading decisions
and to send the trading orders using computers
and low latency informatics systems.
The questions we are asking today about the
investment in the capital markets are more
elaborated: how to analyze the real-time price
evolution in order to have a profit edge? How
to decide when to enter the capital market?
How much to buy and how to manage and
limit the capital risk? How to build exit
decisions based on price behavior? How to
organize all of these into an informatics
system? And how to optimize all computing
processes in order to maximize the profit and
to minimize the involved risk? This paper will
try to answer to all these questions presenting
a complete trading methodology that can be
tracked and applied by anyone in order to
build an algorithmic trading system.
One particular specificity of this paper is that
all presented methods, algorithms and rules
will be referred for short and medium time
trades. This means the trades are open and
kept for different periods of time, between
minutes to even hundreds of hours. The
purpose of this methodology is to make a
profit on a longer period of time speculating
some special market conditions as we will see.
Starting from this fact, some readers can
consider this paper dedicated rather to
investment methods on the capital markets
1
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than to the short trading methodologies.
Regardless of the used term, the presented
system will make the profit from both short
and medium term trades. The efficiency level
obtained will prove the relevance of the
presented algorithms which can be adapted
and optimized for any financial market.
To answer the question when are the best
entry moments and how to analyze the time
price series in order to build the entry
decisions, this paper will present the
Cyclicality Trading Method, an original
method based on the “Price Cyclicality
Function” [2]. The new model will be
compared with two other known methods that
can be applied in the same market conditions.
One was introduced by Larry Connors and
Cezar Alvarez in 2009 using the 2-periods
Relative Strength Index, presented as “the
trades’ holy grail of indicators” [3] and the
second method is based on the very well-
known Bollinger Bands [4].
To build the exit decisions this paper will
introduce a simple and proved closing strategy
based on the price behavior. The Combined
Exit Method includes two profit levels and
real-time price action in order to optimize
trading efficiency. The presented exit
methodology can also be optimized for any
capital market to maximize the profit and to
reduce the capital exposure level regarding the
investors requirements.
In order to build an algorithmic trading
software, the entry and exit methods presented
will be assembled into buyng and sell trading
signals, which are Boolean variables used to
automate the trading decisions. The logical
structure of the trading informatics system
will be presented together with the real-time
data streams used to access and compute the
time price series and to convert it into low-
latency trading signals.
Analyzing the comparative results included in
the last part of the article we can classify the
Cyclicality Trading Method used with
Combined Exit Method as a reliable trading
methodology. Together with the suitable risk
management procedure, the presented
algorithms can be used in order to design a
profitable trading software for any capital
market.
2 Algorithmic trading system
An algorithmic trading system, in the
acceptance of this paper, is a software
implemented by the investor in direct
connection with the informational brokerage
system. We can call this on short as trading
software. It is specially designed to receive
and analyze the real-time price and the capital
data streams, to build the trading signals using
different data mining models, to decide about
the trading volume using a capital
management procedure and to build and to
send the trading orders to the brokerage
system.
Fig. 1. Data streams and logical modules of an algorithmic trading system.
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The logical modules and data streams
included in an algorithmic trading system are
presented in figure 1. This paper will present
a mathematical model for the data mining
module. The capital and risk management to
decide the traded volume can be made using
the “Global Stop Loss” [5] method. This
methodology permits to have several
simultaneous open positions made by the
same trading model and to manage and
optimize the capital exposure for each traded
market and for a specified risk level.
One of the main requests for trading software
is the low-latency response. The speed to
assemble and send the trading orders is the
most important factor in order to have a
reliable trading software. The orders must
arrive in the informational brokerage system
before a significant price change, otherwise,
the trading orders will be ignored. The trading
orders are assembled based on the trading
signals and the trading volume using a data
structure provided and accepted by the
brokerage system. Using fast speed data
connections or different application
programming interfaces, the orders are
automatically sent to the brokerage systems.
Usually, the accepted delay between the price
data reception and the order sent is between
10 and 100 milliseconds. When the buy and
sell decisions are also made automatically,
without any human intervention, we will have
an automated trading system.
3 Trading with the time price series
To trade on the capital market, in the
acceptance of this paper, means to buy a
specified volume of shares at a certain price in
a precise moment of time and to sell the same
volume of equities at another moment of time
with a different price. From a mathematical
point of view, a trade is defined by:
 
sellsellbuybuy tpVpt ,,,,
(1)
where
buy
t
and
buy
p
are the buy time and price,
V
is the traded volume and
sell
t
and
are
the sell time and price. Note that using a
contract for difference, the sell operation can
be made before the buy transaction. In the
formula (1) the time order between the buy
and the sell operations is not important.
Three decisions are involved to complete the
variables in the formula (1). They are about
the time and price for the buy operation, about
the volume traded and about the sell time and
price. As we mentioned, the decision about
the trading volume can be made using the
“Global Stop Loss” method [5]. This will
provide the exact value for each traded
volume. This paper will present hot the buy
and sell decisions can be automated.
To decide about the buy and the sell variables
we have to analyze the time price evolution.
This is usually provided by the brokerage
informational system as a repetitive stream
including:
 
meAsk,Bid,ti
(2)
where Ask is the current buy quote, Bid is the
current sell quote and the time is the current
moment of time of the stream component. The
data array (2) is repeated for each moment of
time; the difference between two moments of
time being variable and very short, of the
order of a few milliseconds. To facilitate the
low-latency data processing, the history of the
time price evolution is stored by the brokerage
or by the trading system in data collections
with a different structure:
 
timeframetimeLHCO ,,,,,
(3)
where O is the open price, meaning the quote
level at time; C is the close time, meaning the
quote level at the moment time+timeframe; H
is the highest value of the price and L is the
lowest value of the price between time and
time+timeframe. Using the structure (3) the
data transfer can be made the fastest possible.
In the data array given by (3) there are
included a large number of information given
by the stream arrays delivered by formula (2)
between time and time+timeframe. Changing
the timeframe we can have an accurate
description of the price evolution for each
interval. The timeframe can be any time
interval between seconds, minutes, hours to
days, weeks, month and even years. In
addition, the close price value of the last
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interval is the current quoted price.
The stream data (2) is transformed and stored
into the stream data (3) which will be the data
input for the data mining process presented in
this paper. The trading signals are functions of
the data stream (3) taking Boolean values. For
example, a buy signal will be described as:
  
false iscondition buy if
trueiscondition buy if e
,,,,, false
tru
timeframetimeLHCOftimeBuySingal
(4)
For the exit decisions, an exit condition must
be tested for each time moment, based on the price evolution included in the stream (3). The
exit signals are assembled similarly as:
 
false iscondition exit if
trueiscondition exit if e
,,,,, false
tru
timeframetimeLHCOgtimegalExitBuySin
(5)
Usually, the signals are noted depending on
the index of the data array in the price stream
(3) using indices as
 
timeBuySignalBuySignali
and
 
timegalExitBuySinExitSignali
. Note that
the stream (3) includes the current quote level
once it is received in real-time. This will
permit to build the buy and exit signals with
low latency in order to have an instant
decision system. For the markets where sell
trades can be considered before the buy
operations, the sell signals and the exit from
the sell trades can be assembled in the same
way. In this paper, we will develop and
present only buy trades. The main objective of
the presented method is to trade shares and
indices on the stock markets. For this case, the
long trades give us better efficiency. The data
mining methods will mathematically define
the conditions included in the formulas (4)
and (5) in order to complete the trading
methodology.
4 The Cyclical Trading Method
This trading method is developed starting
from the three basic ideas about the capital
investments mentioned at the beginning of
this paper. The method purpose is to find those
price levels where we can buy cheap and sell
more expensive after a period of time. The
patience principle will be inserted into the
presented methodology by keeping the open
positions for a longer period of time until an
efficiency level is achieved. The
unpredictability of the price behavior makes
hard to evaluate the precise time interval to
make a profit and to meet the efficiency level.
This fact excludes the time interval to be a
design requirement. Consequently, this
method is not suitable for high-frequency
trading systems.
The Cyclical Trading Method starts from the
idea that in any market the price is increasing
for a period of time. After an increased
interval, the investors start to mark their profit
and to close their positions. The selling orders
will produce a price decreasing which
determines a descending interval. After a
time, when the price is lower, more and more
investors start to buy again, determining
accordingly a new increasing interval. The
cyclic behavior of the quoted price can be
observed in any capital market for any
timeframe. A mathematically function
describing the price cyclic behavior is the
Price Cyclicality Function (PCY)
introduced in [2]. Looking in figure 2. we can
see the price evolution together with the PCY
function. It can be observed the PCY function
is ascending when the price is growing and
decreasing when the price is decreasing. The
minimal points of the PCY function are
located where the price makes local minimum
values.
To entry in the markets when the price is
lower means to buy near the minimal point of
the PCY function. This will generate cyclic
entries using the simple trading condition
made by:
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 
ii PCYBuySignal
(6)
The ξ parameter will define the maximal value
of the PCY function when the algorithmic
trading system will start to buy shares. This
functional parameter can be optimized for
each financial market depending on different
efficiency criteria. Looking at the graph
presented in figure 2. we can see that the price
can decrease more after the ξ value is achieved
in the intervals where the PCY function is
approaching to make a minimum value. This
means that better entry points can be found
after the first moment when
i
PCY
. To
speculate all these better entries, the
algorithmic trading software will initiate
several buy trades with the lower price once
the (6) condition is still valid. In order to
distribute capital exposure, the additional
trades will be decided by the additional
trading signal:
 
1kkkk ppPCYBuySignal
with
Mk 1
(7)
where k define each price level
k
p
when the
quotes decreased with δ distance under the last
entry and M is the maximal number of trades.
The functional parameters δ and M can be
optimized for each traded market using
different optimization methods.
Fig. 2. Cyclicality price behavior. Extreme price levels detected by different methods.
The methodology implies not to trade and
wait until the PCY function decrease under a
specified level ξ. After this trigger is achieved,
more trades will be initiated each time when
the price quote decrease with one more δ
distance under the last entry price. To limit the
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risk, a maximal number of open trades M is
considered. All the trades will be kept open
until a profitable condition will be met. The
exit conditions will be discussed in one future
chapter.
The cyclical trading method permits to initiate
trades on the capital markets in those time
intervals when the price makes minimal
values. The advantage is the lower risk
involved and the good trading efficiency
obtained. The main disadvantage is the long
time period when the model waits for a new
trading opportunity; the numbers of the
generated trades being small.
5 The 2-PERIOD RSI Method
The 2-period RSI [3] method uses the Relative
Strength Index [6] of 2 time periods in order
to build the buy decision. The buy signals are
built when the RSI value decrease under a
specified value:
 
ii RSIBuySignal
(8)
where α can take small values in order to
locate those intervals when the price makes
lower values. The RSI signals can be fallowed
in figure 2. It was found that this methodology
makes good trading signals but time to time it
generates false signals in almost all capital
markets. An example is also included in figure
2. On the left side of the graph, the RSI made
a minimal value but the price continues to
increase for another 10-12 intervals and after
that significantly decreased under the entry
point. In this case, the risk level involved in
that trade is very high. This fact damaged the
trading efficiency of the 2-period RSI method.
These cases can be filtered using also the PCY
function. Imposing a maximal value for the
PCY function when the 2-period RSI signal is
considered, we will have better results given
by:
 
iii PCYRSIBuySignal
(9)
where π defines the PCY filter level. For most
of capital markets, a common value for the π
functional parameter is
50
. In figure 2 is
presented the price evolution of the Frankfurt
Stock Exchange Deutscher Aktienindex
DAX30 [7] for the first ten months of the 2018
year using the daily timeframe. The additional
trading signals will be generated by:
   
1kkkkk ppPCYRSIBuySignal
with
Mk 1
(10)
where M is the maximal number of open
trades and δ is the considered price step.
6 Lower price with Bollinger Bands
Another function that can be used in order to
locate the time intervals when the price takes
local minimum values is the Bollinger
function [4]. In figure 2. are figured over the
price graph the 2 standard deviation Bollinger
bands for 20 time intervals period. Time to
time the price values are below the lower
Bollinger band. The trade trigger will be
activated the first time when the price
decreases under the lower band. The trading
signal is given by:
 
iii LBBpBuySignal
(11)
where
i
p
is the current ask price and
 
i
LBB
is the lower Bollinger band
calculated for σ standard deviation. The
parameter σ can have any positive value and it
will be the subject of an optimization process
in order to increase the trading efficiency for
each traded market.
In order to filter the same false trading signals
explained in the previous chapter, an
additional PCY filter will be added. In the
same way, the trading signal will be generated
by:
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 
iiii PCYLBBpBuySignal
(12)
and the repetitive trading entries will be considered using the condition:
 
1kkkkkk ppPCYLBBpBuySignal
with
Mk 1
(13)
where δ is price step used to add new trades
and the M is the maximal number of the
trades.
7 Combined Exit Method
Trading on the capital market involves an exit
decision. The profit made by the algorithmic
trading system is also the difference between
the buy price and the selling price. In order to
build the exit decision, several exit
methodologies can be found in the literature.
A comparative presentation is included in [3].
Some of the most used methods are fixed time
exit strategy, fixed profit level exit strategy,
first up-close exit strategy, seven up-close exit
strategy, new high exit strategy, close above
the moving average exit strategy and 2-period
RSI exit strategy. All of these are presented
and compared in [3].
This paper will present the Combined Exit
Method using the 2-period RSI function in
order to integrate the current price action and
two profit levels for different cases. It was
found that the best trading efficiency using the
entries presented above is obtained with the
exit condition:
ii
ii
iRSINProfit
RSINProfit
nalExitBuySig if
if
(14)
where N is the number of the current open
trades, 1 < N < M, φ and ψ are two desire
profit levels for the two cases, usual φ > ψ and
Ω is a level of the 2-period RSI function where
the market is considered overbought. In the
formula (14)
 
N
kkiki BidAskVProfit 0
(15)
is the total profit in the i moment of time,
computed as sum of the individual profit of all
the N open trades,
k
V
is the volume of each
trade,
k
Bid
is the entry price for each trade
and
i
Ask
is the asked price level in the current
moment of time.
The logical description for this exit
methodology derives from the principle of
patience needed in the stock market in order
to make a profit. Once initiated the trading
process, on the first time interval until the
market is not overbought
 
i
RSI
, the
algorithmic trading system waits to catch the
φ profit level for each open trade. If this
purpose was not achieved and the market
evolved in such way to be considered
overbought
 
i
RSI
, a lower ψ profit level
is considered and marked in order to close all
opened positions before the market to turn
into a descending interval. Usually the 50 < Ω
< 90, depending on the traded market.
The most important advantage of the exit
conditions made by formula (14) is that it can
be optimized for any financial market using
the functional parameters φ, ψ and Ω, and it
can be applied for any number N of the open
trades. The exit strategy permits to have
longer intervals in order to record higher
profit levels, as consequence to the patience
principle included.
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8 Code samples
Sample code for the algorithm integration is
presented in figure 3. The used language is
MetaQuotes programming language [8]
designed to implement trading algorithms
under MeraTrader platform [9].
In the presented code, the start() procedure is
repeated at any time when the current quote
price is changed. No trade is opened until the
EntryTrigger gets the TRUE value which is
initiated by the trading signals generated with
formula (6), (9) or (12). Once a trade was
opened, the DELTA distance from the last
open price is tested in order to add new
positions. Before the entry process, the current
profit is computed and compared with the
desired profit levels. Once a profit level is
achieved, regarding the formula (14), all
trades are closed and the trading software
entry into the waiting phase until a new
Trigger condition is met. As we can see in
figure 3, implementing all the presented
formulas can be done in simple steps.
Fig. 3. Algorithm integration sample code in MetaQuotes programming language.
9 Comparative results
In this section are presented trading results
obtained with the entry signals (6), (9) and
(12) together with the exit signals generated
by the formula (14). The results were obtained
using TheDaxDealer [10], an automated
trading system that uses all the presented
methodologies in order to trade the Frankfurt
Stock Exchange Deutscher Aktienindex
DAX30 [7]. The results presented in table 1
were obtained between 01.12.2016 and
30.11.2018.
The DAX30 index was traded as a contract for
differences with a spread of 1 point. The
exposed capital involved and the risk
management were accomplished using the
“Global Stop Loss” [2] method with a
maximal exposure capital level of 1%. All the
data mining methods were applied for a daily
timeframe. The test trading capital considered
was 1.000.000 $ and an additional condition
was imposed regarding the hourly intervals of
the executed trades between 7:00 and 21:00
coordinated universal time (UTC) to trade on
a liquid market.
Table 1. Trading results for DAX30 index in a time interval of 24 months.
Entry type
Profit
Drawdown
Risk to
Reward
Number
of trades
Longest
trade
Price Cyclicality
30,369
8,583
1:3.54
249
424 hours
Relative Strength Index
11,307
9,469
1:1.19
45
214 hours
Bollinger Bands
18,293
8,851
1:2.07
47
141 hours
All signals together
43,834
9,713
1:4.51
282
424 hours
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In table 1. are presented the trading results
obtained for the next values of the functional
parameters:
- Price Cyclicality signals given by (6) with
ξ=16;
- 2-period Relative Strength Index signals
given by (9) with α=4 and π=50;
- Bollinger Bands trading signals given by
(12) with σ=2 and π=50;
- all signal together with the same values for
the functional parameters.
The exit decisions were assembled using the
formula (14) with Ω=50, φ=150, ψ=20 and
M=10. The capital evolution into the test
trading account for all signals assembled
together is presented in figure. 4. for 24
months interval.
Fig. 4. Capital evolution for DAX30 trading index in a time interval of 24 months.
As it was already mentioned, the main
disadvantage of the presented methodology is
the reduced number of trades. Looking for
those time intervals when the price takes
minimal values, the presented trading
methodology does not make any trade for long
periods of time. In order to have a real image
of this aspect, the no open trade time intervals
were computed and presented in table 2.
Table 2. Trading results for DAX30 index in a time interval of 24 months.
Entry type
Maximal
no trade time
Total no
trade time
Total
trading time
Trading capital
time efficiency
Price Cyclicality
2,351 hours
14,864 hours
2,656 hours
15.16%
Relative Strength Index
3,289 hours
15,629 hours
1,891 hours
10.79%
Bollinger Bands
3,528 hours
15,529 hours
1,991 hours
11.36%
All signals together
2,351 hours
14,073 hours
3,447 hours
19.67%
10 Comments and conclusions
To compare the trading results obtained with
all three entry models we have to analyze the
numbers presented in table 1. The trading
efficiency and the number of trades made with
the Cyclical Trading Method are higher. Even
the longest time trade is higher, the risk to
reward ratio obtained with the cyclicality
methodology is 1:3.54, a considerable value
for a 24-month investment with the maximal
capital exposure of only 1%. We have to
observe that the longest time trade is 424
hours, between two and three weeks, a good
time interval for a medium-term strategy.
Comparing the results obtained with the same
capital and risk conditions, we can say that the
Cyclicality Trading Method is better than the
2-period RSI method which was for many
years one of the most preferable trading
strategies. The entry model using the
Bollinger bands makes the shortest trades.
From this point of view, this is the method that
places the trigger entry to the nearest point
from the minimum local prices. In the test
presented, the method using the Bollinger
bands obtained a better reward for the same
risk level as the 2-period RSI model. Played
together, all three methods will produce a
better profit for the same capital exposure.
The total risk to reward ratio obtained with all
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three methodologies is 1:4.51, a good value
when it is about an automated trading
software set up with the maximal capital risk
of 1%. Having all of these considerations and
results, the question how to analyze the time
price series and how to decide when is better
to entry in the capital market got the answer:
using the Cyclicality Trading Model. The 2-
period RSI and the Bollinger bands are still
valid trading models with reasonable risk to
reward ratio, methods which can increase the
total trading efficiency of the algorithmic
trading system.
As we mentioned, risk management was made
using the Global Stop Loss method. The
model permits to have more open trades at the
same time. This is a sustained answer to the
question about how to manage the risk and the
exposed capital. In addition, the Combined
Exit Method offers us the answer to the
question regarding exit decisions. The
presented exit strategy permits to insert and
implement into the mathematical algorithms
the principle of patience in trading and the
behavior and the current price action. All
presented models can be optimized using
different methodologies in order to maximize
the trading efficiency and to minimize the risk
level accordingly the investors requirements.
A special note is regarding the simplicity of
the trading models presented and the reduced
number of the functional parameters. This will
permit easy adaptability of this methodology
for any financial markets and will permit the
use of this model in any algorithmic trading
environment. In addition, the reduced number
of calculations needed will contribute to the
low-latency response with small resources.
The Cyclicality Trading Model together with
the Combined Exit Model includes all the
basic trading principles. The models buy
when the capital market is near the minimum
values, include the patience principle waiting
on markets for higher profit opportunities and
also include the unpredictability of the price
behavior closing the longest trades when the
market is approaching the overbought
intervals.
The methodology presented in this paper was
tested, implemented and used with the same
good results for a representative number of
financial markets: Deutscher Aktienindex
(DAX30), Dow Jones Industrial Average
(DJIA30), Financial Times London Stock
Exchange (FTSE100), Cotation Assistée en
Continue Paris (CAC40), Swiss Stock
Exchange Market Index (SMI20), Australian
Securities Exchange Sydney Index
(ASX200), Tokyo stock Exchange Nikkei
Index (Nikkei225), NASDAQ100 Index,
Standard & Poor’s Index (S&P500) and Small
Capitalization US Index (Russell2000). Also
with good and stable results, the Cyclical
Trading Method presented in this article
together with the Combined Exit Model was
applied with good and sustained results for
Gold and Bent Crude Oil markets.
Looking at the numbers in table 2. We can
have some conclusions about capital usage
time. From the total time allocated in the test
results, the capital is involved in a trade for
15,16% of the time using the Cyclical Trading
Model, higher than the 2-period RSI and
Bollinger methodologies. Even so, using all
the presented methods, the capital is involved
in the trading activity for only 19,67 of the
time. This means more than 80% of the time
the capital is not used. This is the most
important disadvantage of the presented
methodology. To avoid and improve this
aspect, the presented methods are used in
practice together with other trading models to
make additional trades when the capital is not
used by current methods.
As final conclusions, the Cyclical Trading
Method together with the Combined Exit
Method gives us an important profit edge for
investing in the capital markets. These
methods include all the basic principles of the
financial trading: the entry price is near the
minimum values, the trades are kept in order
to catch higher profit levels and the price
action is also included to close the trades when
the price behavior is changing. The low-risk
level involved by entering in the markets near
the minimum price intervals permits to obtain
a reliable risk to reward ratio achieved in short
and medium trading time. The presented
methodology can be adapted for algorithmic
trading systems and can be optimized for any
36 Informatica Economică vol. 23, no. 1/2019
DOI: 10.12948/issn14531305/23.1.2019.03
capital markets.
References
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Confusiones, Portions Descriptive of the
Amsterdam Stock Exchange, translated by
Hermann Kellenbenz. Barcelona, Spain:
Profit Editorial (2009), ISBN13:
9788496998957.
[2] Păuna, C., Lungu, I. (2018). Price
Cyclicality Model for Financial Markets.
Reliable Limit Conditions for Algorithmic
Trading, Studies and Economic
Calculations and Economic Cybernetics
Journal, vol. 4/2018. ISSN: 0585-7511.
[3] Connors, L., Alvarez, C. (2009). Short
Term Trading Strategies That Work. A
Quantified Guide to Trading Stocks and
ETFs, US: TradingMarkets Publishing
Group. ISBN: 978-0-9819239-0-1.
[4] Bollinger, J. (2002). Bollinger on
Bollinger Bands. The Seminar. The
essentials. US: Bollinger Capital
Management. DVD. ISBN: 978-0-
9726111-0-7.
[5] Păuna, C. (2018). Capital and Risk
Management for Automated Trading
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Iași, Romania. Available at:
https://pauna.biz/ideas
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Cristian PĂUNA graduated the Faculty of Cybernetics, Statistics and
Economic Informatics of the Economic Studies Academy in 1999 and he is
also a graduate of the Aircraft Faculty from the Bucharest Polytechnic
University in 1995. He got the title of Master of Science in Special Aerospace
Engineering in 1996. In the last decades, he had a sustained activity in the
software development industry, especially applied in the financial trading
domain. Based on several original mathematical algorithms, he is the author
of more automated trading software for financial markets. At present, he is Research and
Development Manager of Algorithm Invest company and he is involved as a Ph.D. student in
the Economic Informatics Doctoral School from the Bucharest University of Economic Studies.
... A particular approach for risk management techniques that can be used in automated decision-making systems for capital investments can be found in (Vince, 1992). Mathematical models especially designed and optimized for algorithmic trading with proved and sustained results in real capital investments can be found in (Păuna & Lungu, 2018), (Păuna, 2018a), (Păuna, 2018b), (Păuna, 2018c), (Păuna, 2019a), (Păuna, 2019b), (Păuna, 2019c), (Păuna, 2019d), (Păuna, 2019e), (Păuna, 2019f), and (Păuna, 2020). ...
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After several attempts to publish my Ph.D. thesis with different prestigious publishers, I have decided to make this work public and free of charge for anyone. Enjoy! Cristian Păuna
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Capital investment is a sustained activity nowadays. After the worldwide release of the electronic trading systems, automated decision-making investment software is the new trend in financial speculation. A significant part of capital trading is fully computerized today. The buying and selling orders are made and sent automatically, almost in real-time. The price evolution is analyzed by servers using advanced mathematical algorithms. This chapter will present one of these models named Price Probability Predictor. It is a method to build a probability field based on the price history and the real-time price action. The revealed function will generate the current probability of a price growth in the next time intervals. Automated entry and exit signals and market limit conditions will be built using the new indicator, in order to automate the whole investment process. Capital investment results will also be included in the current paper to qualify the presented trading methodology and to compare it with other similar models. In conclusion, it was found that the Price Probability Predictor is a reliable mathematical algorithm that can assist any trading decisions, in both ways, manual or automatic capital investments.
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Using automated capital investment software systems is a common task today. At the beginning of the third millennium, modern investors are using artificial intelligence resources and methods to find the best investment opportunities on capital markets and to process the trading orders. One of the most important aspects of this activity, besides the buying and selling decisions, is to stay away from the market risk in specific conditions. For this purpose, in the current doctoral research, the notion of limit conditions in capital markets was introduced by the authors. On the high price volatility markets, when the economic or geopolitical background is changing fast, real-time decisions for earlier investment closing, or filtering decision not to open new positions in specific market states, will contribute together to the risk reduction and will provide a higher capital efficiency a the long time run. In the real-time investment software systems, the limit conditions method's implementation presumes particular aspects in order not to introduce additional time delays for the trading orders. This paper will present the way how to include additional limit conditions procedures into automated algorithmic trading software systems. It was found that any investment strategy can be improved by using the limit conditions methods presented in this paper. Based on particular data-mining methods applied to real-time price series of any market, these methods can be automated and included in any capital investment informatics systems in order to improve the results and to reduce the allocated capital risk.
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Confusion de Confusiones, Portions Descriptive of the Amsterdam Stock Exchange, translated by Hermann Kellenbenz
  • J De La Vega
De la Vega, J. (1688). Confusion de Confusiones, Portions Descriptive of the Amsterdam Stock Exchange, translated by Hermann Kellenbenz. Barcelona, Spain: Profit Editorial (2009), ISBN13: 9788496998957.
Short Term Trading Strategies That Work. A Quantified Guide to Trading Stocks and ETFs
  • L Connors
  • C Alvarez
Connors, L., Alvarez, C. (2009). Short Term Trading Strategies That Work. A Quantified Guide to Trading Stocks and ETFs, US: TradingMarkets Publishing Group. ISBN: 978-0-9819239-0-1.
Bollinger on Bollinger Bands. The Seminar. The essentials. US: Bollinger Capital Management
  • J Bollinger
Bollinger, J. (2002). Bollinger on Bollinger Bands. The Seminar. The essentials. US: Bollinger Capital Management. DVD. ISBN: 978-0-9726111-0-7.