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Scientific Guide to Equilibrium Fractal Wave

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Scientific Guide to Equilibrium Fractal Wave

Written Date: 22 Sep 2018

Article Version 1.2

By Young Ho Seo
Quantitative Developer and Financial Engineer
 admin@algotrading-investment.com

www.algotrading-investment.com

1. Introduction to Equilibrium Fractal Wave

The concept of Equilibrium Fractal Wave was first introduced in the book: Financial Trading with Five Regularities of Nature: Scientific Guide to Price Action and Pattern Trading (Seo, 2017). At that time, the book was written for the pure motivation to identify the important market dynamics for financial traders. The concept of Equilibrium Fractal Wave was born by combining two scientific areas including time series and fractal analysis. The main propositions in the Equilibrium Fractal Wave include:

1. The separate or combined analysis of trend and Fractal wave is possible.
2. The repeating patterns in Equilibrium Fractal Wave are equivalent to the infinite number of distinctive cycles because the scale of the repeating pattern varies infinitely.
3. Equilibrium Fractal Wave is just a superclass of all the periodic wave patterns we know.

First, let us demonstrate the equilibrium fractal wave for readers. The easiest way to demonstrate the equilibrium fractal wave is through the pattern table presented in Figure 1 (Seo, 2017). Many applied researchers in time series and statistics will agree that patterns in the column 1, 2, 3 and 4, from first regularity to fourth regularity, are the mainly extracted features and patterns in their everyday research and operation. It is also agreeable that cyclic wave pattern can co-present with trend together. This concept is the main assumption behind the classic decomposition theory in the time series analysis. In the time series pattern table created by Gardner in 1987 (Figure 2) represents this concept clearly. The first row in the pattern table (Figure 1) shows the data in which no trend or weak trend exists. The second, third and fourth rows shows the co-existence of trend and waves.

Until now, many forecasting or industrial scientists use such concept to build forecasting models. Likewise, there are many applied software to create the forecasting or prediction model of this kind. Some example forecasting software with such modelling capability includes:
1. Stata (www.stata.com)
2. Eviews (www.eviews.com)
3. IBM SPSS (www.ibm.com/products/spss-statistics)
4. SAS (www.sas.com)
5. MatLab (www.mathworks.com)
6. And many others

 
Figure 1: Five Regularities and their sub price patterns with inclining trends. Each pattern can be referenced using their row and column number. For example, exponential trend pattern in the third row and first column can be referenced as Pattern (3, 1) in this table.

 
Figure 2: The original Gardner’s table to visualize the characteristics of different time series data (Gardner, 1987, p175). Gardner assumed the three components including randomness, trend and seasonality in this table.

Now the fifth column in Figure 1 presents the equilibrium fractal wave. This is extended part from the original Gardner’s table. When we list the equilibrium fractal wave in the fifth column, we can see that the pattern table (Figure 1) shows a systematic pattern. From left column to right column, we can see that the number of distinctive cycles in the data increases. For example, we can assume the pure trend does not have any periodic cycle. Therefore, number of the distinctive cycle is zero for pure trend series. Under the second and third columns, we can have one to several distinctive cycles depending on if the series follows daily, monthly, and yearly cycles. Under fourth column, we can have many more distinctive cycles outside daily, monthly and yearly cycles but the number of the cycles is finite. Fourier analysis or principal component method can be used to reveal the number of cycles for any series under column 4. From column 1 to column 4, you might be following this systemic pattern pretty well.
However, you might question why equilibrium fractal wave in column 5 possesses such infinite number of distinctive cycles. This is indeed the right question to ask. To understand this, you have to understand the fractal wave first.

A lot of research on fractal analysis was done by B. Mandelbrot (1924-2010). The Book: fractal geometry of nature (Kirkby, 1983) describes the nature of fractal geometries in scientific language. What is the difference between fractal wave and equilibrium fractal wave in this article? Fractal wave views a series as the subject of fractal analysis. Equilibrium Fractal wave views a series as the co-subject of fractal analysis and trend analysis. Hence, equilibrium fractal wave believes co-existence of trend and wave pattern in a single data series. The significance of equilibrium fractal wave is that we can model the trend and fractal wave in two separate steps or in one-step.
Indeed, scientists use the two-step process to model the data in column 2, 3 and 4 in economic and financial research. For example, price series under column 4 can be modelled with trend in the first step. Then the reminding data can be modelled using cycles in the second step. Likewise, for a data series under column 5, we can model a trend part first, then we can model a fractal wave patterns in separate steps. This explains the Proposition 1. This also imposes the fractal analysis under non-stationary condition when the trend component is strong in the data series. In this case, two-step modelling process might be advantageous. When the trend component is less dominating comparing to fractal wave component, the entire price series can be modelled using fractal analysis only. Proposition 1 states that the choice on the modelling process, either one-step or two-steps, is conditional upon the characteristics of the price series.

In the Book: fractal geometry of nature (Kirkby, 1983), the main characteristics of fractal wave is described as the repeating patterns in varying scales. To give you some idea of repeating patterns in varying scales, we can create a synthetic data like that using Weierstrass function. This function is famous for being continuous everywhere but non-differentiable nowhere among the math community. Of course, real world data will never look like this. However, this synthetic data describe what is repeating pattern in varying scale very well for our readers in Figure 3. You will see the same patterns everywhere in the data. Small pattern are combined to become the bigger pattern. The resulting bigger patterns look the same like small patterns. As the combing process continues, the size of the pattern can increase infinitely. This is referred to as repeating patterns in varying scale or varying size. This is the core assumption on any fractal analysis.

Now let us walk backwards from this combining process. Let us assume that we can extract those patterns in the same scale from rest and we can put them on the separate paper for each scale. When we separate those patterns in the smallest scale from rest, then the extracted series become the first cycle of our data. This extracted series with one cycle is not different from data or a series in column 2, 3 and 4. Likewise, we can separate the second smallest patterns from rest. This will become second cycle of our data. In this time, the frequency of second cycle will be less comparing to the first cycle because the period of second cycle is greater than first cycle. We can keep continue this separating process to create another cycles. Since we can combine to create the repeating patterns infinitely, we can separate the repeating pattern infinitely too. This describes the proposition 2, the infinite number of distinctive cycle.

 
Figure 3: Weierstrass function to give you a feel for the Fractal-Wave process. Note that this is synthetic Fractal-Wave process only and this function does not represent many of real world cases.

Now the Proposition 2 can lead to the Proposition 3 naturally. As you can see from Figure 4, from left to right columns, the number of distinctive cycle increases. Therefore, it is not so hard to say that equilibrium Fractal Wave is a superclass of all the periodic wave patterns we know in column 1, 2, 3 and 4. Figure 4 shows this concept clearly to our reader.
 
Figure 4: Visualizing number of distinctive cycle periods for the five regularities. Please note that this is only the conceptual demonstration and the number of cycles for second, third and fourth regularity can vary for different price series.

Finally, in many real world data, we do not possess the highly regular patterns as in a synthetic data like that using Weierstrass function in Figure 3. The highly regular repeating patterns are described as the stick self-similarity in In the Book: fractal geometry of nature (Kirkby, 1983). Instead of the strict self-similarity, the real world data will form loose self-similarity shown in Figure 5. For the financial price series, we can observe the repeating zigzag patterns made up from so many triangles. The triangles are only similar. However, each triangle in the data will be never identical to the other triangles. This is the typical example of loose self-similarity. This sort of loose self-similarity is much harder to model comparing to the strict self-similarity shown in a synthetic data like that using Weierstrass function (Figure 3).

 
Figure 5:  Loose self-similarity in the financial price series.

2. Empirical Research on Equilibrium Fractal Wave

As we have described, the concept of equilibrium fractal wave allow us to model the series as the co-subject between trend and fractal wave or as the single subject of fractal wave. The modelling choice will depend on the characteristics of data. Regardless of the modelling choice, Empirical research on equilibrium fractal wave must concern the fractal patterns in data series. Empirical research on equilibrium fractal wave in the price series data is relatively small because mainstream academic research is based on the algorithm utilizing the entire data sets like multiple regression techniques instead of detecting patterns.

One exception is the financial trading community. In the trading community, the repeating patterns or repeating geometry was used as early as 1930s. Some pioneers include R. Schabacker (1932), H.M. Gartley (1935) and R.N. Elliott (1938) in time order. In their books, the various repeating patterns were described for various US stock market data (Figure 6, 7 and 8). Until now, millions of traders are using these patterns in their practical applications for the profiting purpose in forex, future, and stock markets. Figure 6, 7 and 8 shows the commonly used repeating patterns by the financial trader. Having said that these repeating patterns in Figure 6, 7 and 8 were not modelled as the co-subject between trend and fractal wave. Instead, those repeating patterns are only modelled as the subject of fractal wave. Only exception is the trend filtered ZigZag indicator and excessive momentum indicator created recently (Seo, 2018). This is understandable consequence because the idea of equilibrium fractal wave and the two-step modelling process were only introduced in 2017. The modelling technique using trend and fractal wave patterns are only available recently. One very purpose of this article is to inform you that it is possible to model the financial price series as the co-subject between trend and fractal wave in two separate steps.

At the same time, another purpose to create equilibrium fractal wave was to connect the contemporary science to many repeating patterns used by the financial traders. Considering that millions of the financial traders now use the repeating patterns for their every day trading, this is a phenomenal level of activity by the society. Many traders are much happier to use the repeating patterns than the traditional math or technical indicators. Unfortunately, the connection between the repeating patterns and the contemporary science is very poor. It seems no literature is positioning those repeating patterns in the scalable scientific framework. Neither the financial trading community have much idea on what these repeating patterns are and why they are using these patterns. Simply speaking the communication between two communities is blocked. If R.N. Elliott (1938) had a chance to meet B. Mandelbrot (1924-2010), then things may have changed bit. However, they lived in two different time.

The pattern table in Figure 1 shows that repeating patterns are merely the extended concept from the conventional mathematical knowledge. We know that it is not so hard to put these five regularities together under the same table. Potential for academic and applied research in equilibrium fractal wave is huge. The main concern is that many techniques used for periodic wave pattern analysis may not work with equilibrium fractal wave because of the infinite number of the distinctive cycle in the data. To the best knowledge, Fourier analysis and many other similar techniques will not handle the infinite number of the distinctive cycle. Therefore, developing new analytical techniques remain as the main challenge for the empirical research in equilibrium fractal wave. In many cases, the algorithm or pattern recognition modelling the price series as the co-subject of trend and fractal wave will improve the prediction accuracy much more.

 
Figure 6: List of triangle and wedge patterns.

 
Figure 7: Ascending Triangle pattern found in USDCAD in H1 chart.

 
Figure 8: Repeating Gartley patterns in Hourly EURUSD Chart Hourly.

3. Further ideas in the Modified Quantum Physics

This section discusses the separate concern from this article. However, this is the last purpose for this article. As we know, Fourier analysis and the quantum mechanics have a strong connection. Fourier analysis can be used to decompose a typical quantum mechanical wave function. The wave and trend concept in Figure 1 closely resemble the wave and particle duality of the quantum physics. For example, the price series with periodic cyclic wave in column 2, 3 and 4 (Figure 1) can be modelled well using Fourier analysis too. Likewise, the trend and particle shares many common analysis techniques in the statistics, signal processing, and object-tracking field too.

As we can extend the classic wave pattern into equilibrium fractal wave pattern (Figure 1), we might be able to extend the quantum physics further to deal with the infinite number of distinctive cycles as in the concept of equilibrium fractal wave. It is often heard that many quantum physics or quantum mechanics based algorithms fail to bring the profits or good prediction in the financial trading. The reason might be that the contemporary quantum physics is not dealing with the infinite number of distinctive cycles present in the data. I am just guessing that the modified quantum mechanics might work much better in the financial trading than the contemporary quantum physics. As a bonus, the modified quantum physics can lead to the technological breakthrough in developing better medicine and better spaceship in the future. This is just some research ideas for those working in physics.
 

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Simple Explanation on Repainting, Recalculating, and Static Algorithm in Technical Analysis

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Simple Explanation on Repainting, Recalculating, and Static Algorithm in Technical Analysis for the Financial Trading
www.algotrading-investment.com

3 Feb 2018

Written By Young Ho Seo
Finance Engineer and Quantitative Trader

The technical analysis is a key to successful trading. Even if you are a fundamental trader, you will need to use technical analysis for the precise control of your entry and exit in your trading. If we count the usage of every technical analysis on the earth, nearly at least a half billion of traders will use technical analysis. The problem is that not everyone is using the technical analysis in the right manner. The purpose of this article is to clear the overly spread misunderstanding about what people called “Repainting technical indicators” in the community. At the beginning, I thought that it would be only matter for starters. Later, I met many forex traders claiming 3 to 5 years of trading experience. However, most of these traders still do not have much clue what is really the repainting indicator except small portion of traders among them. Search on google was disappointing too. Some articles poorly explained on the topic of the repainting. Some articles were almost uninformative to continue to read. Some articles were almost devastated many of excellent technical analysis by some language of witch-hunting. Especially the affected technical analysis on those witch-hunting include:
• Market Profile (invented by J. Peter Stdidlmayer)
• Fractal indicator (invented by Bill Williams)
• Fourier transform and many other signal processing algorithm (invented by Joseph Fourier and many others)
• ZigZag indicator
• Fast moving average including many zero-lag or non-lag moving average family
• Harmonic Pattern (invented by H.M. Gartley, any many others later on)
• Other technical analysis algorithm
The above technical analysis and their algorithm are used by several millions of traders and scientists every day. If you are doubt, just google to look for the internet community using those technical analysis. If those technical analysis and their algorithms are repainting and bad, then why so many people are using them? Well, I think that this will remain as a myth to you until you can clear the misunderstanding about the repainting indicator.
What is really a repainting indicator?
Firstly, what does the repainting means? In the Cambridge dictionary, “repaint” is a verb with a meaning “to paint something again”. In Collins dictionary, “repaint” have a meaning “to apply a new or fresh coat of paint”. The meaning of repainting is almost identical in both dictionary. The example provided by the Cambridge dictionary is:
“The white walls were repainted in pastel shades.”
Two examples provided by the Collins dictionary are:
“Now they kill the crew, repaint and rename the ship, change the flag and papers and steal the cargo, and any other cargo they can find.” (Robert Wilson, INSTRUMENTS OF DARKNESS, 2002)
“But before that – in just an hour or two – a squad of men from the RASC were going to arrive to repaint the interior of the hospital.” (Aldiss Brian, SOMEWHERE EAST OF LIFE, 2002)
You can tell that the term “repainting” is often used to remove or to hide old colours or patterns on the surface by applying new fresh coat of paint. Based on this, in the repainting indicator, the indicator lines or values are repainted every time so that old indicator lines or values can not be found any longer. Is this the case for the above technical analysis algorithm?
Simple answer is no. The above algorithms have nothing to do with repainting. Above technical analysis algorithms keep the old indicator lines or values as they are. Just the latest values can change. For example, in the case of the daily market profile, except today’s market profile, all the past market profile will remain the same. It does not matter how many days you go back to the past, all the past market profile will remain the same. Then why the latest value or indicator line can change? It is because the algorithm is doing recalculation while the latest price is updating in the last candle bar.
The repainting indicator will not keep any old indicator lines or old values since repainting will override all the past values to something new. Literally, the repainting indicator is the random indicator due to some serious bugs or internal logic problem inside the indicator. When the repainting happens, 9 out of 10, it is due to some irritating bugs inside the algorithm.
However, there is also human problem too about the repainting indicator. It is because people use the term “repainting” and “recalculating” interchangeably on the net. This is incorrect and false information. It might start with one or few trader who do not have much experience in trading at the beginning. However, I can tell that this misunderstanding was growing and spreading fast like virus on the net last few years.
Now, if you can tell the difference between repainting and recalculating, then it is good. If not, still do not worry. We will tell you how to differentiate the repainting and recalculating indicators. The best way to differentiate between repainting and recalculating indicator is by asking this question “Does technical analysis algorithm keeps the old values (or old indicator lines) unchanged except the latest value?”  Now consider the simple moving average with the period of 10 as shown in Figure 1. The latest moving average value can change as the new price arrives. The rest of moving average value will stay the same. Likewise, in Figure 2, the latest fractal value can change as the new price arrives. However, except the first fractal, rest of fractals will not change. Likewise, in Figure 3, the first zigzag value can change as the new price arrives. However, except the first zigzag value, rest of zigzag will not change. The same goes for the market profile and other technical analysis algorithm.

 
Figure 1: Simple Moving average with the period 10 in EURUSD.
 
Figure 2: Fractal indicator in EURUSD.

 
Figure 3: Zigzag indicator in EURUSD.

 
Figure 4: Market profile indicator on EURUSD.

Why not avoiding recalculating?
Now one might ask. Can we avoid recalculating? Well, yes you can avoid the recalculating simply by not calculating your algorithm over the last candle bar or by not generating the last value of the indicator. This is called a static algorithm because they are not responsive to the latest price value. For example, simply imagine that if the indicator calculates your moving average values except the first candle bar, then you will get the static moving average indicator. Such a moving average indicator will not have any responsiveness to the new price arrivals. It is static. You can achieve the same by just using open price of the candle bar. Likewise, if you calculate the fractals from the second candle bar, then you will get the static fractal indicator too. For the fractal indicator, you cannot use open price because you need either high or low price of the candle bar. For some technical analysis algorithm, just ignoring the latest candle bar is not sufficient to turn the indicator to static. Some indicators like zig zag or market profile requires certain length of data to calculate one indicator value. In that case, you can simply skip to generate latest value and generate from the second values. For example, if you skip today’s market profile and generate the market profile from yesterday, then you will have the static market profile too. Likewise, you can generate your zigzag from second value too skipping to generate the first zigzag value. If your indicator or pattern detection scanner is using the zigzag indicator, you can also turn them into static one by using the zigzag values from second one (i.e. using the static zig zag).
With the static algorithm or static indicator, you can avoid recalculating. Well sounds easy and wonderful. However, you will experience a serious problem soon. The problem is that you are the only one looking at the lagging information whereas all the other traders are working with the decent latest information for more profits. For example, if you are looking at yesterday’s market profile alone, then you will not able to find what is happening today. All disciplined trader will work with yesterday’s market profile as well as today’s market profile. Likewise, if you detect harmonic patterns with the statics zigzag indicator, then you can only detect the patterns after many candle bars. In Figure 5, you can tell that you do not have any advantage of using the static zigzag indicator to detect harmonic patterns. Especially using the static zigzag indicator, your Reward/Risk ratio will be very poor. You can only detect the harmonic pattern after the price has moved too much in the direction using the static zigzag indicator. Recalculating zigzag indicator will report the appearance of harmonic pattern way faster than the static zigzag indicator. With recalculating zigzag indicator, you have a much better opportunity to enter the market while the sufficient profit is left for you. So do you still prefer the static indicator? Well the choice is entirely up to you.

 
Figure 5: Harmonic Pattern Detection timing using recalculating zigzag indicator and static zigzag indicator.

How Harmonic Pattern Plus and Price Breakout Pattern Scanner help you to achieve the best performance for your trading?
Our Harmonic Pattern Plus (and Harmonic Pattern Scenario Planner) and Price Breakout Pattern Scanner uses the recalculating algorithm to find the latest pattern faster. When the pattern is detected, you will still have an opportunity to enter for the sufficiently good reward/risk ratio for your trading. Yes, they can change if new high or new low price arrive to the market. However, we provide the locking feature to help your trading. This means that you can pin down the pattern in your chart. Once you pin down the pattern in your chart, you do not have to worry about to lose the pattern in your chart because they will stay in your chart forever. To do so, simply click on the “Lock” button in your chart.
 
Figure 6: Harmonic Pattern Plus (Harmonic Pattern Scenario Planner) locking feature.

 
Figure 7: Price Breakout Pattern Scanner locking feature.
Link to Harmonic Pattern Plus (Harmonic Pattern Scenario Planner) and Price Breakout Pattern Scanners.
• https://algotrading-investment.com/portfolio-item/harmonic-pattern-plus/
• https://algotrading-investment.com/portfolio-item/harmonic-pattern-scenario-planner/
• https://algotrading-investment.com/portfolio-item/price-breakout-pattern-scanner/

Technical Indicator Library Excel Formula

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Technical Indicator Library Excel formula

Below we list Excel formula to call technical indicator library from your Excel. All these technical indicator functions are located inside TechnicalAnlaysis.xll file. TechnicalAnalysis.xll files are free to use and free to share without any limitation. We have put some friendly Copy Right Notice on the bottom of this document to protect the developers and contributor. In general, this TechnicalAnalysis.xll file and Technical Indicator library inside the file can be used by anyone and it is free of charge. To use these functions from your Excel, you should load the TechnicalAnlaysis.xll add-in to your Excel first. For the paid users for Quant Strategy Inventor, the installation can be done automatically when you first load our Quant Strategy Inventor. For free users of this TechnicalAnlaysis.xll, please follow the simple installation steps below.

1. Install TechnicalAnalysis.xll file
To install TechnicalAnlaysis.xll file, go to Options in your Excel. Then select Add-ins.

When the Add-Ins manager pop up, click on Browse button and select the TechnicalAnalysis.xll file from your hard drive.

Once TechnicalAnalysis.xll files are loaded in your Excel. You can call any of User Defined Function below to build various trading strategies from your Excel. Above installation step can be skipped for paid users of our Quant Strategy Inventor. Below, we list the all the available Technical and Mathematical Function you can call with TechnicalAnalysis.xll file.
2. Example Usage of Functions

All the functions are array formula. Therefore, you have to enter these formula using “Ctrl +Shift+Enter” keys. You should include “=TA_” syntax before Function name.

For example, for following Bollinger Bands function below:

BBANDS – Bollinger Bands
upperband, middleband, lowerband = BBANDS(close, timeperiod=5, nbdevup=2, nbdevdn=2, matype=0)
You will enter “=TA_BBANDS(I7:I30, 12, 2, 2, 1)” to range L7:N30 assuming your price data are located at the range E6:K30.

We can take another example for CCI function as shown below.
CCI – Commodity Channel Index
real = CCI(high, low, close, timeperiod=14)
Here is how to put this CCI function in your worksheet. “=TA_CCI(G7:G30, H7:H30, I7:I30, 13)” to range L7:L30 assuming your price data are located at the range E6:K30.

3. Overlap Studies Functions

BBANDS – Bollinger Bands
upperband, middleband, lowerband = BBANDS(close, timeperiod=5, nbdevup=2, nbdevdn=2, matype=0)

DEMA – Double Exponential Moving Average
real = DEMA(close, timeperiod=30)

EMA – Exponential Moving Average
real = EMA(close, timeperiod=30)

HT_TRENDLINE – Hilbert Transform – Instantaneous Trendline
real = HT_TRENDLINE(close)

KAMA – Kaufman Adaptive Moving Average
real = KAMA(close, timeperiod=30)

MA – Moving average
real = MA(close, timeperiod=30, matype=0)

MAMA – MESA Adaptive Moving Average
mama, fama = MAMA(close, fastlimit=0, slowlimit=0)

MAVP – Moving average with variable period
real = MAVP(close, periods, minperiod=2, maxperiod=30, matype=0)

MIDPOINT – MidPoint over period
real = MIDPOINT(close, timeperiod=14)

MIDPRICE – Midpoint Price over period
real = MIDPRICE(high, low, timeperiod=14)

SAR – Parabolic SAR
real = SAR(high, low, acceleration=0, maximum=0)

SAREXT – Parabolic SAR – Extended
real = SAREXT(high, low, startvalue=0, offsetonreverse=0, accelerationinitlong=0, accelerationlong=0, accelerationmaxlong=0, accelerationinitshort=0, accelerationshort=0, accelerationmaxshort=0)

SMA – Simple Moving Average
real = SMA(close, timeperiod=30)

T3 – Triple Exponential Moving Average (T3)
real = T3(close, timeperiod=5, vfactor=0)

TEMA – Triple Exponential Moving Average
real = TEMA(close, timeperiod=30)

TRIMA – Triangular Moving Average
real = TRIMA(close, timeperiod=30)

WMA – Weighted Moving Average
real = WMA(close, timeperiod=30)

4. Oscillator Indicators

ADX – Average Directional Movement Index
real = ADX(high, low, close, timeperiod=14)

ADXR – Average Directional Movement Index Rating
real = ADXR(high, low, close, timeperiod=14)

APO – Absolute Price Oscillator
real = APO(close, fastperiod=12, slowperiod=26, matype=0)

AROON – Aroon
aroondown, aroonup = AROON(high, low, timeperiod=14)

AROONOSC – Aroon Oscillator
real = AROONOSC(high, low, timeperiod=14)

BOP – Balance Of Power
real = BOP(open, high, low, close)

CCI – Commodity Channel Index
real = CCI(high, low, close, timeperiod=14)

CMO – Chande Momentum Oscillator
real = CMO(close, timeperiod=14)

DX – Directional Movement Index
real = DX(high, low, close, timeperiod=14)

MACD – Moving Average Convergence/Divergence
macd, macdsignal, macdhist = MACD(close, fastperiod=12, slowperiod=26, signalperiod=9)

MACDEXT – MACD with controllable MA type
macd, macdsignal, macdhist = MACDEXT(close, fastperiod=12, fastmatype=0, slowperiod=26, slowmatype=0, signalperiod=9, signalmatype=0)

MACDFIX – Moving Average Convergence/Divergence Fix 12/26
macd, macdsignal, macdhist = MACDFIX(close, signalperiod=9)

MFI – Money Flow Index
real = MFI(high, low, close, volume, timeperiod=14)

MINUS_DI – Minus Directional Indicator
real = MINUS_DI(high, low, close, timeperiod=14)

MINUS_DM – Minus Directional Movement
real = MINUS_DM(high, low, timeperiod=14)

MOM – Momentum
real = MOM(close, timeperiod=10)

PLUS_DI – Plus Directional Indicator
real = PLUS_DI(high, low, close, timeperiod=14)

PLUS_DM – Plus Directional Movement
real = PLUS_DM(high, low, timeperiod=14)

PPO – Percentage Price Oscillator
real = PPO(close, fastperiod=12, slowperiod=26, matype=0)

ROC – Rate of change : ((price/prevPrice)-1)*100
real = ROC(close, timeperiod=10)

ROCP – Rate of change Percentage: (price-prevPrice)/prevPrice
real = ROCP(close, timeperiod=10)

ROCR – Rate of change ratio: (price/prevPrice)
real = ROCR(close, timeperiod=10)

ROCR100 – Rate of change ratio 100 scale: (price/prevPrice)*100
real = ROCR100(close, timeperiod=10)

RSI – Relative Strength Index
real = RSI(close, timeperiod=14)

STOCH – Stochastic
slowk, slowd = STOCH(high, low, close, fastk_period=5, slowk_period=3, slowk_matype=0, slowd_period=3, slowd_matype=0)

STOCHF – Stochastic Fast
fastk, fastd = STOCHF(high, low, close, fastk_period=5, fastd_period=3, fastd_matype=0)

STOCHRSI – Stochastic Relative Strength Index
fastk, fastd = STOCHRSI(close, timeperiod=14, fastk_period=5, fastd_period=3, fastd_matype=0)

TRIX – 1-day Rate-Of-Change (ROC) of a Triple Smooth EMA
real = TRIX(close, timeperiod=30)

ULTOSC – Ultimate Oscillator
real = ULTOSC(high, low, close, timeperiod1=7, timeperiod2=14, timeperiod3=28)

WILLR – Williams’ %R
real = WILLR(high, low, close, timeperiod=14)

5. Volume Indicators

AD – Chaikin A/D Line
real = AD(high, low, close, volume)

ADOSC – Chaikin A/D Oscillator
real = ADOSC(high, low, close, volume, fastperiod=3, slowperiod=10)

OBV – On Balance Volume
real = OBV(close, volume)

6. Volatility Indicators

ATR – Average True Range
real = ATR(high, low, close, timeperiod=14)

NATR – Normalized Average True Range
real = NATR(high, low, close, timeperiod=14)

TRANGE – True Range
real = TRANGE(high, low, close)

7. Price Transformation

AVGPRICE – Average Price
real = AVGPRICE(open, high, low, close)

MEDPRICE – Median Price
real = MEDPRICE(high, low)

TYPPRICE – Typical Price
real = TYPPRICE(high, low, close)

WCLPRICE – Weighted Close Price
real = WCLPRICE(high, low, close)

8. Cycle Indicator Functions

HT_DCPERIOD – Hilbert Transform – Dominant Cycle Period
real = HT_DCPERIOD(close)

HT_DCPHASE – Hilbert Transform – Dominant Cycle Phase
real = HT_DCPHASE(close)

HT_PHASOR – Hilbert Transform – Phasor Components
inphase, quadrature = HT_PHASOR(close)

HT_SINE – Hilbert Transform – SineWave
sine, leadsine = HT_SINE(close)

HT_TRENDMODE – Hilbert Transform – Trend vs Cycle Mode
integer = HT_TRENDMODE(close)

9. Pattern Recognition Functions

CDL2CROWS – Two Crows
integer = CDL2CROWS(open, high, low, close)

CDL3BLACKCROWS – Three Black Crows
integer = CDL3BLACKCROWS(open, high, low, close)

CDL3INSIDE – Three Inside Up/Down
integer = CDL3INSIDE(open, high, low, close)

CDL3LINESTRIKE – Three-Line Strike
integer = CDL3LINESTRIKE(open, high, low, close)

CDL3OUTSIDE – Three Outside Up/Down
integer = CDL3OUTSIDE(open, high, low, close)

CDL3STARSINSOUTH – Three Stars In The South
integer = CDL3STARSINSOUTH(open, high, low, close)

CDL3WHITESOLDIERS – Three Advancing White Soldiers
integer = CDL3WHITESOLDIERS(open, high, low, close)

CDLABANDONEDBABY – Abandoned Baby
integer = CDLABANDONEDBABY(open, high, low, close, penetration=0)

CDLADVANCEBLOCK – Advance Block
integer = CDLADVANCEBLOCK(open, high, low, close)

CDLBELTHOLD – Belt-hold
integer = CDLBELTHOLD(open, high, low, close)

CDLBREAKAWAY – Breakaway
integer = CDLBREAKAWAY(open, high, low, close)

CDLCLOSINGMARUBOZU – Closing Marubozu
integer = CDLCLOSINGMARUBOZU(open, high, low, close)

CDLCONCEALBABYSWALL – Concealing Baby Swallow
integer = CDLCONCEALBABYSWALL(open, high, low, close)

CDLCOUNTERATTACK – Counterattack
integer = CDLCOUNTERATTACK(open, high, low, close)

CDLDARKCLOUDCOVER – Dark Cloud Cover
integer = CDLDARKCLOUDCOVER(open, high, low, close, penetration=0)

CDLDOJI – Doji
integer = CDLDOJI(open, high, low, close)

CDLDOJISTAR – Doji Star
integer = CDLDOJISTAR(open, high, low, close)

CDLDRAGONFLYDOJI – Dragonfly Doji
integer = CDLDRAGONFLYDOJI(open, high, low, close)

CDLENGULFING – Engulfing Pattern
integer = CDLENGULFING(open, high, low, close)

CDLEVENINGDOJISTAR – Evening Doji Star
integer = CDLEVENINGDOJISTAR(open, high, low, close, penetration=0)

CDLEVENINGSTAR – Evening Star
integer = CDLEVENINGSTAR(open, high, low, close, penetration=0)

CDLGAPSIDESIDEWHITE – Up/Down-gap side-by-side white lines

integer = CDLGAPSIDESIDEWHITE(open, high, low, close)

CDLGRAVESTONEDOJI – Gravestone Doji
integer = CDLGRAVESTONEDOJI(open, high, low, close)

CDLHAMMER – Hammer
integer = CDLHAMMER(open, high, low, close)

CDLHANGINGMAN – Hanging Man
integer = CDLHANGINGMAN(open, high, low, close)

CDLHARAMI – Harami Pattern
integer = CDLHARAMI(open, high, low, close)

CDLHARAMICROSS – Harami Cross Pattern
integer = CDLHARAMICROSS(open, high, low, close)

CDLHIGHWAVE – High-Wave Candle
integer = CDLHIGHWAVE(open, high, low, close)

CDLHIKKAKE – Hikkake Pattern
integer = CDLHIKKAKE(open, high, low, close)

CDLHIKKAKEMOD – Modified Hikkake Pattern
integer = CDLHIKKAKEMOD(open, high, low, close)

CDLHOMINGPIGEON – Homing Pigeon
integer = CDLHOMINGPIGEON(open, high, low, close)

CDLIDENTICAL3CROWS – Identical Three Crows
integer = CDLIDENTICAL3CROWS(open, high, low, close)

CDLINNECK – In-Neck Pattern
integer = CDLINNECK(open, high, low, close)

CDLINVERTEDHAMMER – Inverted Hammer
integer = CDLINVERTEDHAMMER(open, high, low, close)

CDLKICKING – Kicking
integer = CDLKICKING(open, high, low, close)

CDLKICKINGBYLENGTH – Kicking – bull/bear determined by the longer marubozu
integer = CDLKICKINGBYLENGTH(open, high, low, close)

CDLLADDERBOTTOM – Ladder Bottom
integer = CDLLADDERBOTTOM(open, high, low, close)

CDLLONGLEGGEDDOJI – Long Legged Doji
integer = CDLLONGLEGGEDDOJI(open, high, low, close)

CDLLONGLINE – Long Line Candle
integer = CDLLONGLINE(open, high, low, close)

CDLMARUBOZU – Marubozu
integer = CDLMARUBOZU(open, high, low, close)

CDLMATCHINGLOW – Matching Low
integer = CDLMATCHINGLOW(open, high, low, close)

CDLMATHOLD – Mat Hold
integer = CDLMATHOLD(open, high, low, close, penetration=0)

CDLMORNINGDOJISTAR – Morning Doji Star
integer = CDLMORNINGDOJISTAR(open, high, low, close, penetration=0)

CDLMORNINGSTAR – Morning Star
integer = CDLMORNINGSTAR(open, high, low, close, penetration=0)

CDLONNECK – On-Neck Pattern
integer = CDLONNECK(open, high, low, close)

CDLPIERCING – Piercing Pattern
integer = CDLPIERCING(open, high, low, close)

CDLRICKSHAWMAN – Rickshaw Man
integer = CDLRICKSHAWMAN(open, high, low, close)

CDLRISEFALL3METHODS – Rising/Falling Three Methods
integer = CDLRISEFALL3METHODS(open, high, low, close)

CDLSEPARATINGLINES – Separating Lines
integer = CDLSEPARATINGLINES(open, high, low, close)

CDLSHOOTINGSTAR – Shooting Star
integer = CDLSHOOTINGSTAR(open, high, low, close)

CDLSHORTLINE – Short Line Candle
integer = CDLSHORTLINE(open, high, low, close)

CDLSPINNINGTOP – Spinning Top
integer = CDLSPINNINGTOP(open, high, low, close)

CDLSTALLEDPATTERN – Stalled Pattern
integer = CDLSTALLEDPATTERN(open, high, low, close)

CDLSTICKSANDWICH – Stick Sandwich
integer = CDLSTICKSANDWICH(open, high, low, close)

CDLTAKURI – Takuri (Dragonfly Doji with very long lower shadow)
integer = CDLTAKURI(open, high, low, close)

CDLTASUKIGAP – Tasuki Gap
integer = CDLTASUKIGAP(open, high, low, close)

CDLTHRUSTING – Thrusting Pattern
integer = CDLTHRUSTING(open, high, low, close)

CDLTRISTAR – Tristar Pattern
integer = CDLTRISTAR(open, high, low, close)

CDLUNIQUE3RIVER – Unique 3 River
integer = CDLUNIQUE3RIVER(open, high, low, close)

CDLUPSIDEGAP2CROWS – Upside Gap Two Crows
integer = CDLUPSIDEGAP2CROWS(open, high, low, close)

CDLXSIDEGAP3METHODS – Upside/Downside Gap Three Methods
integer = CDLXSIDEGAP3METHODS(open, high, low, close)

10. Statistics Functions

BETA – Beta
real = BETA(high, low, timeperiod=5)

CORREL – Pearson’s Correlation Coefficient (r)
real = CORREL(high, low, timeperiod=30)

LINEARREG – Linear Regression
real = LINEARREG(close, timeperiod=14)

LINEARREG_ANGLE – Linear Regression Angle
real = LINEARREG_ANGLE(close, timeperiod=14)

LINEARREG_INTERCEPT – Linear Regression Intercept
real = LINEARREG_INTERCEPT(close, timeperiod=14)

LINEARREG_SLOPE – Linear Regression Slope
real = LINEARREG_SLOPE(close, timeperiod=14)

STDDEV – Standard Deviation
real = STDDEV(close, timeperiod=5, nbdev=1)

TSF – Time Series Forecast
real = TSF(close, timeperiod=14)

VAR – Variance
real = VAR(close, timeperiod=5, nbdev=1)

11. Math Transform Functions

ACOS – Vector Trigonometric ACos
real = ACOS(close)

ASIN – Vector Trigonometric ASin
real = ASIN(close)

ATAN – Vector Trigonometric ATan
real = ATAN(close)

CEIL – Vector Ceil
real = CEIL(close)

COS – Vector Trigonometric Cos
real = COS(close)

COSH – Vector Trigonometric Cosh
real = COSH(close)

EXP – Vector Arithmetic Exp
real = EXP(close)

FLOOR – Vector Floor
real = FLOOR(close)

LN – Vector Log Natural
real = LN(close)

LOG10 – Vector Log10
real = LOG10(close)

SIN – Vector Trigonometric Sin
real = SIN(close)

SINH – Vector Trigonometric Sinh
real = SINH(close)

SQRT – Vector Square Root
real = SQRT(close)

TAN – Vector Trigonometric Tan
real = TAN(close)

TANH – Vector Trigonometric Tanh
real = TANH(close)

12. Math Operator Functions

ADD – Vector Arithmetic Add
real = ADD(high, low)

DIV – Vector Arithmetic Div
real = DIV(high, low)

MAX – Highest value over a specified period
real = MAX(close, timeperiod=30)

MAXINDEX – Index of highest value over a specified period
integer = MAXINDEX(close, timeperiod=30)

MIN – Lowest value over a specified period
real = MIN(close, timeperiod=30)

MININDEX – Index of lowest value over a specified period
integer = MININDEX(close, timeperiod=30)

MINMAX – Lowest and highest values over a specified period
min, max = MINMAX(close, timeperiod=30)

MINMAXINDEX – Indexes of lowest and highest values over a specified period
minidx, maxidx = MINMAXINDEX(close, timeperiod=30)

MULT – Vector Arithmetic Mult
real = MULT(high, low)

SUB – Vector Arithmetic Substraction
real = SUB(high, low)

SUM – Summation
real = SUM(close, timeperiod=30)

TechnicalAnlaysis.xll file is free to use for everyone and redistributable without any limitation. To protect the developers and contributors, the following copyright notice should be included when this file is redistributed or when the file is used.
THIS SOFTWARE IS PROVIDED “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE DEVELOPERS AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Instruction (Manual) Document

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1. Information about Author
Your Surname ATI
Your First Name   ATI
Your Country ATI
Your Email Address ATI
Your ID on our website ATI

2. Information for the submitted materials
Title of the submitted instruction or manual Technical Indicator Library Excel Formula
Language of Instruction English
Key words (at least 3) Forex, Stock, Investment, Trading, optimization, simulation, backtesting, technical analysis, economic analysis, Quantitative Trading
Date of Completion 21 October 2016
Version of this Document 1.0

3. If it is about any trading platform or any of our products (leave empty if you don’t use)
Name of Trading Platform Quant Strategy Inventor
Trading Platform version Version 5.16R
Name of Product Quant Strategy Inventor
Product version 5.16R

Portfolio Selection Theory By Harry Markowitz

Basic Math and Statistics for Finance and Investment

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Basic Math and Statistics for Finance and Investment

Following equations are partially applicable for the benefit of your Trading and Investment but not compulsory. Normally these equations are quite basic for solving many finance and investment problems in real world sense. “Introductory Statistics” and “Time value of Money” parts should be understood by all traders and investors before they trade on real live trading. It is our recommendation even though many traders skip these parts.

1. Introductory Statistics

N = number of observation

Mean, 

Population variance, 

Population standard deviation, 

Population Covariance = 

Sample variance, 

Sample standard deviation, 

Sample covariance =  

Correlation Coefficient, r =   using sample covariance.

2. Time Value of Money

Rate of return (ROR)

Rate of return, 
Where

C1 = realization of investment at the end of the year
C0 = investment at the beginning of the year

Future value of a single sum

Future value, 

Where

PV = principal or present value of a single sum
r = interest rate
n = number of compounding periods

Present value of a single sum

Present value, 

Where

FV = future value or cash flow at the end of period n
r = discount rate
n = number of compounding periods

Future value of a series of cash flows

Future value, 

Where

Ct = Cash flow at the end of period n
r   = interest rate
n  = number of compounding periods

Present value of a series of cash flows
Present value, 

Where

Ct = Cash flow the end of period n
r   = interest rate
n  = number of compounding periods

Net present value

Net present value,   if the capital outlay occurs only at the beginning of the project

Net present value,   if the capital outlay occurs in different years of the project

Where

CO = the capital outlays at the beginning of the project
COt = the capital outlays at end of period n
Ct = Cash flow the end of period n
r   = interest rate
n  = number of compounding periods

Present value of a perpetuity

Present value of a perpetuity, 

Where

P   = the cash flow received/paid under annuity (i.e. periodic payment)
r    = the compound interest rate per period

Internal rate of return (IRR)

The internal rate of return is the discount rate that makes net present value equal to zero.

Where

Cn = Cash flow the end of period n
IRR = internal rate of return
n = period

3. Compounding Interest basics

Amount in compound interest
Amount,   or 
Where
i = r/k = interest rate per period
n = kt = total number of conversion periods

Where
r = nominal interest rate per year
k = number of conversion periods per year
t = number of years (or term)

Present value in compound interest

Amount in continuous interest

Amount, 

Where
e = natural base = 2.718281828

Present value in continuous interest

Present value, 

4. Effective Interest Rate

Annual percentage rate (= nominal annual interest rate)

Annual percentage rate, 

Where
i = rate per compounding period
n = number of compound periods in a year

Effective annual interest rate in compound interest transaction

Effective annual interest rate, 

Where

r = nominal (= simple) interest rate per year (= APR)
k = number of conversions per year

Effective annual interest rate in continuous interest transaction

Effective annual interest, 

Where

r = nominal (=simple) interest rate per year (=APR)

5. Annuity Equations

Future value of an ordinary annuity

Future value of an ordinary annuity, 
Where

P   = the cash flow received/paid under the annuity (i.e. periodic payment)
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Present value of an ordinary annuity

Present value of an ordinary annuity,  

Where

P   = the cash flow received/paid under annuity (i.e. periodic payment)
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Periodic payment into a sinking fund (=future value)

Periodic payment, 

Where

FV = the future value to meet
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Future value of an annuity due

Future value of an annuity due, 

Where
P   = the cash flow received/paid under the annuity
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Present value of an annuity due

Present value of an annuity due, 
Where

P   = the cash flow received/paid under annuity (i.e. periodic payment)
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Present value of a deferred annuity

Present value of a deferred annuity,
 

P   = the cash flow received/paid under annuity (i.e. periodic payment)
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period
x   = the number of period before the first cash flow

Present value of a perpetuity

Present value of a perpetuity, 

Where

P   = the cash flow received/paid under annuity (i.e. periodic payment)
r    = the compound interest rate per period

Instruction (Manual) Document

This part should be filled by author before your submission.

1. Information about Author
Your Surname ATI
Your First Name   ATI
Your Country ATI
Your Email Address ATI
Your ID on our website ATI

2. Information for the submitted materials
Title of the submitted instruction or manual Basic Math and Statistics for Finance and Investment
Language of Instruction English
Key words (at least 3) Finance, Forex, Stock, Investment, Trading, Future
Date of Completion July 2016
Version of this Document 1.0

3. If it is about any trading platform or any of our products (leave empty if you don’t use)
Name of Trading Platform MS-Excel, SAS, SPSS
Trading Platform version 
Name of Product 
Product version 

ATI Registration Request Form for Training

Setting up Push Notification with Smart Phone from your MetaTrader

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Setting up push Notifications to receive notification with your Smart Phone from your MetaTrader

From our experience, push notification is better than email notification when you want to be notified with your Smart phone from Desktop MetaTrader. Here is how to configure your push notification from your Desktop or Laptop MetaTrader to your mobile version of MetaTrader using MetaQuotes ID. With this configuration, you can receive notification or alert to your Smart Phone from your Desktop or Laptop MetaTrader.
• Install Mobile version of Meta Trader terminal to your Smart Phone
• From your mobile version of Meta Trader terminal, go to “Settings” >> Message >> obtain “Meta Quotes ID”. It is mixed letters and numbers like 9443BFF. Write down this ID to somewhere in your note for later use.

• Enter your MetaQuotes ID from your Mobile MetaTrader to your Desktop MetaTrader. In your Desktop MetaTrader, go to Tools >> Options >> Notification >> Enter your MetaQuotes ID. (We assume that you have already installed Desktop MetaTrader to your computers.)
• Ok. Everything is done. If you are successful, then you will receive some notification with your Smart Phone when your EA send alerts using push notifications. Most of our products have the built in feature of Push Notifications.
Instruction (Manual) Document

This part should be filled by author before your submission.

1. Information about Author
Your Surname ATI
Your First Name   ATI
Your Country ATI
Your Email Address ATI
Your ID on our website ATI

2. Information for the submitted materials
Title of the submitted instruction or manual Setting up Push Notification with Smart Phone from your MetaTrader
Language of Instruction English
Key words (at least 3) Forex, Investment, MetaTrader,
Date of Completion 11 May 2015
Version of this Document 1.0

3. If it is about any trading platform or any of our products (leave empty if you don’t use)
Name of Trading Platform MetaTrader 4 or MetaTrader 5
Trading Platform version Build 950
Name of Product
Product version