A simulation-based bayes-procedure for robust prediction of pairs trading strategies

A simulation-based bayes-procedure for robust prediction of pairs trading strategiesClick to see the full-text of:

A simulation-based Bayes’ procedure for robust

prediction of pairs trading strategies

Lukasz T. Gatarek?, Lennart F. Hoogerheide and Herman K. Van Dijk

February 8, 2011

We propose a new simulation method to estimate the cointegration model with

nonnormal disturbances in nonparametric Bayesian framework in order to present a

robust prediction of some alternative trading strategies. We apply the theory of Dirich -

let processes to estimate the distribution of disturbances in form of infinite mixture


The motivation for statistical arbitrage techniques has its roots in works that preach

predictability of stock prices and existence of long term relations in the stock markets.

This literature challenges the stylized fact in financial economics which says that the

stock prices shall be decribed by independent random walk processes; what would au -

tomatically imply no predictability in the stock prices. The key references in this area

are [Lo and MacKinlay, 1988], [Lo, 1991], [Lo and MacKinlay, 1992] and [Guidolin, 2009].

Based on these empirical investigations trading strategies might be formed to explore the

inefficiences of the stock markets.

[Khadani, 2007] consider a specific strategy first proposed by [Lehmann, 1990] and

[Lo and MacKinlay, 1990] that can be analyzed directly using individual U. S. equities

returns. Given a collection of securities, they consider a long/short market-neutral equity

strategy consisting of an equal dollar amount of long and short positions, where at each

rebalancing interval, the long positions consist of losers (underperforming stocks, relative

to come back to equilibrium which is zero. [Gatev et al. 2006] show the performance of

this arbitrage rule over a period of 40 years and they find huge empirical evidence in favour

The crucial steps in building the pairs trading strategy is the local estimation of both

current and expected spreads. In the framework of cointegration analysis spread is modeled

as the local deviation from the long-term equilibrium among the time series. Therefore the

current spread betwenn the assets is computed as the product of cointegrating vector and

current stock prices. On the other hand, the expected spread is estimated as the product

of cointegrating vector and predicted stock prices. The spread prediction is based on the

assumption of sound cointegration relation among the pair of assets. To sum up, the

pairs trading technique is based on the assumption that the linear combination of prices

(scaled by the cointegrating vector) reverts to zero and a trading rule can be constructed

to exploit the expected temporary deviations.

The problems concerning the implementation of this technique may have two main

The paper is constructed as follows.


In order to test the profitability of pairs trading strategy we need to identify long term rela -

tions in the stock prices. Therefore we apply cointegration model, see [Juselius, 2006]. The

distributions of stock market returns are typically nonnormal. Thus usually t-distribution

and other fattailed distributions are applied. In case of pairs trading, we try to identify

cointegrating relations in a huge universe of assets. It might be incorrect to assume com -

mon distribution of returns across different stocks. We propose a general algorithm to

estimate the cointegration model in a Bayesian way under nonnormality. The outline of

such an algorithm is composed as follows

4. Standardize the residuals and construct artificial timeseries ytaccording to

yt= ? yt+ (?t, j? µt, j)/?Vt, j.

5. Go to Step 1 using artificial timeseries.

The challenge to construct such an algorithm lies in finding an accurate method to select

the number of components in the mixture of Normal distributions. The components of

this mixture are different in each repetition of the algorithm. Thus a flexible method for

estimating this mixture is needed.

We propose to model this distribution as a Dirichlet Process Mixture (DPM) - a mix -

ture with a countably infinite number of components. Due to this property this technique

is more flexible than a finite ordered mixture model which ex ante specifies the number

of components. For a general introduction to modelling via Dirichlet processes refer to

Math and forex

Math and forexMath and Forex

So a mathematical law was recently brought to my attention called Bayes Law.

Bayes Law:

Basically a statistical probability calculation based on a set of predefined variables (or historical data) which calculates the statistical probability of event A when event B is true.

The reason I'm interested in this calculation:

I want to study when a candle is X pips in size, what is the probability that it will make it to Y pips in size.

For instance, When I look at the 1hr time frame, I want to know what the probability of a candle that is 25 pips in size will make it to 30 pips in size. I would like someone with indicator coding expertise to create an indicator that can do these calculations for me. I believe I have figured out how to do the math (see below), I just need it to be incorporated in an indicator format. What this will allow any user to do is determine when to enter the market and how may pips to take with high probability. I feel this tool could be useful for both scalping and longer term trades. Could someone please review the information below and let me know how possible this idea is. I think there is some huge potential but I lack the coding knowledge to test it.

My concept that needs to be applied to MT4 coding:

Bayes Law Equation:

P(A|B) = P(B|A)*P(A) / P(B)


P(A|B) = the probability of A, if B is true

P(B|A) = the probability of B, given A is true

P(A) = the probability of A, or how often does A occur?

P(B) = the probability of B, or how often does B occur?

User input Parameters:

Number of candles

Study candle range

Target pip profit

Count number of candles within number of candles whos range is equal to or greater than study candle range parameter. Return a number that defines A. Then compute A/number of candles. This solution defines P(A).

Count number of candles within number of candles whos range is equal to or greater than study candle range + target pip profit. Return a number that defines B. Then compute B/number of candles. This solution defines P(B).

Then compute P(B)/P(A). This solution defines P(B|A).

Then compute P(B|A)*P(A)/P(B). This solution defines P(A|B).

Then display results on the chart.

Items to display on the chart:

Number of Candles

Study Candle Range

Target Pip Profit

Ema prediction

Ema predictionEMA Prediction

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Forex prediction master1

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Trading solutions for Forex

Forex Prediction Master is a convenient software program for trading solutions for Forex. This program will give you positive and negative predictions of the different changes that happen to the market.

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Forex prediction

Forex predictionForex prediction

This example is very similar to the previous one. The only difference is that it shows data for foreign exchange (forex) currency pairs.

How to work with the applet

If you have not seen the first example. please explore it first - basic description is available there.

In this applet, following data are available. All of them are end of day close values for the whole year 2007, i. e. 313 values. As in the previous applet, each of these time series have the following values: zero for interval below 0, close value in the interval 0-number of values, and again zero after the last known value.

EURUSD - EUR USD forex currency pair data

USDJPY - EUR USD forex currency pair data

USDCHF - EUR USD forex currency pair data

EURJPY - EUR USD forex currency pair data

Again note that this example is provided for illustration only. Trading using this simple setup is usually not far away from using prediction by last available value. Also note that for trading we need to develop entry and exit rules, and that they are more important than exact prediction.

Please wait until the applet is loaded.

Online forex predictor megabox

Online forex predictor megaboxOnline Forex Predictor MegaBOX

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Approaches of forex prediction software

Approaches of forex prediction softwareApproaches of Forex Prediction Software

Forex prediction is used to forecast the possible rate of Forex by using the available information. Forex prediction is made by two methods - analyzing the technical and fundamental data. There is no such prediction system that can guarantee a 100% accurate outcome yet software generated predictions are made on the basis of historical data and hypothesis.

How Does Forex Prediction Works

Forex prediction is done by software. It is easy to maneuver and predictions can be obtained at any point of time with the help of a simple click of the computer mouse. This software analyzes the historical data and its patterns. Then, it optimizes the parameters of the system accordingly so that most accurate and fool-proof prediction is generated. It can also backtest the system that you use for trade before venturing into the real market with real money. Once you feed the online results, you will be told the current trends of the market.

Approaches of Forex Prediction

As mentioned earlier, Forex prediction can be done by two approaches - technical and fundamental.

Technical Approach to Forex Prediction

This approach involves relatively small sized data packet from which a particular aspect of the trade is analyzed. Some analyze the patterns in the charts displayed and predict as per the meaning of the pattern stands. These are called chartists. Another parameter of Forex prediction is moving averages of short and long term Forex data. This is a momentum based model where the data is analyzed statistically. Many companies sell data for analysis. You can buy or download the information. Some of the reliable sources are companies like Alarm trades and Technical Research Limited.

Fundamental Approach to the Forex Prediction

There are few economic variables that are at work in the Forex industry. The fundamental approach deals with the foreign exchange rate and the trend of market derived from these variables for Forex prediction. These fundamental variables are rate of savings, prices of stock, trade balance, consumption and surveys of opinion. These variables are analyzed either mathematically by econometric way or being judgmental by personal opinions. For fundamental analysis, you can get the data from investment banks like Barclays and CitiGroup and providers like Reuter.

Why Forex Prediction Software

One of the most crucial parts of Forex trading is the timing for getting in and out. With the software, it becomes lot easier. In normal process, it would take many years and hand on experience to master it, but the Forex prediction software does it for you with real ease. Also, analysis is not something which everyone masters at. You can buy signals from the dealers and brokers too, but that would neither be cost effective nor it would be a great idea to share the profit. But with a good Forex prediction software, you can actually increase your profit because you are paying once and reaping the harvest forever. You save a lot time by not monitoring or analyzing. Once you start up the system and enter the currency information required, you can sit aside and enjoy the cool breeze while software keeps earning for you.

Forex prediction indicator

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Accurate binary options prediction using artificial neural networks

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Improve your trading strategies with rcode for prediction,pair trading,cointegration,back testin

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My Algorithm, Modelling, and Strategy Development courses just keep getting bigger and better. In the next few weeks, Ill be posting R source code to teach you exactly how to:

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Indicator not false signals

Indicator not false signalsTREND PREDICTION

Trend Scalper forex indicator has extremely powerful prediction capabilities, able to tell you exactly when to trade and when not to trade.

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Wavelets for stock market trading and crash prediction

Wavelets for stock market trading and crash predictionJames (view profile)

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Forex predictions and biases

Forex predictions and biasesForex Predictions and Biases

posted by Samuel Rae on August 19, 2014 at 7:24 am

A forex prediction refers to a forecast or an expectation for a particular outcome. When you make a prediction in forex, you are making a call on how an economic report will turn out or how a currency pair will react to it.

Meanwhile, a bias is simply an inclination towards an event that may be more likely to occur. Having a bias is thinking that the dollar could have a bearish or bullish outlook depending on how US economic data turns out.

In forex trading, it is important to have biases but traders are often cautioned against making strong predictions. When you make a forex prediction, it is like you are shutting off other possibilities except for what you are expecting to happen. When you take a trade idea based solely on a prediction, you could hurt your pride if the market shows a different scenario playing out.

A bias, on the other hand, is still open for confirmation. You can have a bias at the start of the week based on previous market themes and dominant price action, but you can leave this up for confirmation by the upcoming data. If your bias is proven wrong, you can just as easily switch sides and take the opposite bias without hurting your psyche.

Remember that the market does not care about your forex prediction. Even if you are proven wrong and hurting from a losing trade, the market will still continue to trade without looking back.

Instead, when you simply keep a bias, you are maintaining an open mind and letting the market dictate how you should trade and how you might be able to profit. Having a bias is being about reactionary than anticipating price action.

Of course its normal to have a certain forex prediction as to how price action will fare since most of the analysis, such as technicals and fundamentals, are geared towards picking which scenarios are more likely to occur. Dont forget though to spend an equal amount of time figuring out how you will manage your trade if actual reports or price action turns out different from what you expected.

At the end of the day, its important to keep an open mind and accept that anything is possible in the forex market. Of equal importance is proper risk management in making sure that you dont lose your money when your bias turns out wrong.

Currency prediction based on apredictive algorithm

Currency prediction based on apredictive algorithmCurrency prediction based on a predictive algorithm.

Forex Forecast: 70% Hit Ratio

The left-hand graph shows June 15th 2014 currency forecast which includes both long and short recommendations. The green boxes signify long signals and the red boxes signify short signals. The bright shades denote the strongest signals. The right-hand side shows the returns of the suggested currency pairs from June 15th 2014 to September 15th 2014.

Forecast Length: 3 Months (6/15/14 9/15/14)

How to interpret this diagram:

Algorithmic Forex

Forecast: The table on the left is the currency forecast produced by I Know Firsts algorithm. Each day, subscribers receive forecasts for six different time horizons. The currencies in the 1-month forecast may be different than those in the 1-year forecast. In the included table, only the relevant currencies have been included. A green box represents a positive forecast, while a red represents a negative forecast. The boxes are then arranged according to their respective signal and predictability values (see below for detailed definitions).

Forecast Performance: The table on the right compares the actual currency performance with I Know Firsts prediction. The column titled Forecast shows which direction the algorithm predicted, and the column % Change shows the actual currencys performance over the indicated time period. The Accuracy column shows a v if the algorithm correctly predicted the direction of the stock or an x if the forecast was incorrect. The I Know First Hit Ratio represents the algorithms accuracy when predicting the trend of the currency.

Signal: This indicator represents the predicted movement direction/trend; not a percentage or specific target price. The signal strength indicates how much the current price deviates from what the system considers an equilibrium or “fair” price.

Predictability: This value is obtained by calculating the correlation between the current prediction and the actual asset movement for each discrete time period. The algorithm then averages the results of all the prediction points, while giving more weight to recent performance. As the machine keeps learning, the values of P generally increase.