Statistical arbitrage and pairs trading on Forex

Does anyone know what formula is used to calculate the difference?

I think more the he have just lose all his money with the strategy thats the reason he have stop to offer it. I know i did code a MT5 EA some years ago for simulat strategy i did backtest GBPUSD with EURUSD and the results was not interesting it did work sometimes but sometimes both pairs have lose korrelation for longer period and the drawdowns where to big.

Look at my picture from MT5 backtest, i think something simular happen with his trading, he did maybe use 2 trades with to much lotsize and then such trends happend which did go complete wrong directions.

You see in the picture first a few good trades but then both trades did go complete wrong, so this is statistical arbitrage, forget it.

If you want to see a rel arbitrage strategy look to my topic: https://www.forexfactory.com/thread/...5-10-per-month

Why don't you continue to discuss such a good post? I think MT4R can be used to statistically calculate currency differences to achieve profit. I hope my friends will continue to discuss

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I couldn't get the forexpairtrading.ex4 tool to work, I tried it on the icmarkets demo account and it didn't work

Employing simple linear regression for pair spread, as thread starter did, won"t work in the long term. The cointegration is a dynamic relationship as well as spread between pairs, so one must utilize some sort of dynamic filtering like Kalman filter in order to get better results.

The pair (or multiplets) trading is usually advertised as risk-free strategy. But it's not.

Like this one below shows EURUSD/USDCHF spread (daily chart with out of sample part from 1st of Jan. 2022):


EURUSD / USDCHF is a well-known pair suitable for pair trading. However, on the picture above, you can see it's not risk-free trading at all. In time of high volatility, the spread can drift a lot (like around March 2021 and May 2022). So risk management is also important here. Mean reversion does not mean it's not requiring SL.

So unfortunately, there are no free lunches :/.

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Finally, here is a chart with Z-Score and the spread for better demonstration.



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Another example can be spread constitutes Light Crude Oil vs. Brent

You actually do not need to calculate the price difference. Pairs trading aka mean reversion is based on the idea that stationary time series return to the mean, with emphasis on stationary. Common time series are not (usually) stationary, but their synthetic combination can be stationary. So, you need to find out time series (2 or more), which combination is stationary, and calculate the spread (synthetic stationary time series) and hedge ratio of the spread constituents.

There are a couple of approaches how to find/construct synthetic stationary time series from common time series.

1. Linear combinations of pairs utilizing Linear Regression (OLS) and Augmented Dickey-Fuller test (ADF)
2. Johansen test for cointegration (Vector Error Correction Model)
3. Kalman filtering
4. Mix of the above

Point 1 above is not good due to several disadvantages like it's only for pairs, i.e., for only 2 time series, it's dependent on what's selected as Y and what as X. The
pair1 = B * pair2 + e is not equal to pair2 = B * pair1 + e. Meaning, we get 2 different results for these 2 regression formulas.

I used to use the MT4R. Indeed, it's a great tool. But I prefer Python over R.

So, the first problem, to find stationary time series, was described. It's feasible by employing some computer program seeking for the time series combinations that are constituting synthetic stationary time series.
Another difficulty, though. Cointegrated pairs need to be trade exactly in calculated hedge ratio. E.g., on the sample for EURUSD and USDCHF I pasted above, we see, we need to buy 1 unit of EURUSD and 2.123 units of USDCHF to create the synthetic time series (the spread).
According to my investigation, there are only two brokers who allow trading units.

1. Oanda → they are really extraordinary here, since they allow trading from 1 unit! This is perfect for this kind of trading. However, they are not cheap (from bid/ask spread perspective)
2. Dukascopy → they allow trading on unit level from 1000 units. E.g., standard MT4 allows trading from 1000 units and up with steps of 1000 (1000, 2000, 12000 etc.), with Dukascopy one can trade e.g., 1209, 3657 units (but not 768 units, i.e., amount < 1000) etc. So Dukascopy is also fairly good broker for mean reversion trading, but need bigger account than with Oanda.

Here I'd like to ask FF community. Is there any other broker allowing trading with units? (no micro-accounts!)

Agree!

It can be stationary for certain periods of time which unfortunately damned hard to find out even with most sophisticated machine learning software.

Below is sample for GU-UC pair trading on M1 time frame.
It is profitable when spread behave to mean-reversion (stationary) from Jan to Mar 2022 showed by increase equity (blue colored area).
But when there are enormous changes in financial market recently e.g., parity of EUR to USD and most likely GBP to USD in near future, spread is trending, and this strategy is not working anymore (indicated by dropping equity from Apr\END).

But it also looks like you had the chance to stop this trading pair combination, because the spread increased much too before even the equity curve dropped that much. That cointegration topic here is something to be done in a cautious manner. Because everytime it can stop work mean-reverting and thus have no cointegration anymore. But then later it can work again. So this have to be measured continously. Previously I wrote that there are suitable pairs for trading, but this is not always the case, as you have shown too. Cointegration comes and goes, so it have to be monitored. Unfortunately I do not see a better way to do the cointegration pairs trading. But over time it should work. Just one more thought about the higher frequency strategy on the 1 min or 5 min timeframe. For me it looks like they are too sensitive when it comes to news, so trading on any high impact news must be avoided. So far I have not seen that smaller timeframes outperform higher timeframes siginificant.

Do Johansn test to find co-integration, use lambda as hedge ratio, build a spread series, normalize it and trade +-2 and close at 0. It's like a small term project for college students.

Hello, traders.
I was wondering if this type of trading is still alive at this point. If anyone is still pursuing it, could we trade emails or discords? I want to discuss some questions with you, experienced pairs traders.

NIce thread

I'm waiting EURCHF / NZDUSD

STATISTICS EURCHF / NZDUSD
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T1 (pvalue) = 0.034
T2 (pvalue) = 0.010
Correlation = 0.819
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I'm waiting SHORT confrmation at close

Last signal:

LOG TRADES
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2023-11-17 00:00:00
- Selling Ratio 1.68448
- Sell AUDCAD 0.89370 Buy NZDCHF 0.53055
2023-11-20 00:00:00
- Selling Ratio 1.68581
- Sell AUDCAD 0.90046 Buy NZDCHF 0.53414

Hi are you here ?

I have been experimenting with pair trading strategy since before it gained attention on this forum, gathering insights and testing strategies. In 2021/2022, I struggled to develop the necessary code for MQL5 due to the absence of ADF, Half-Life, regression codes, and other essentials. Consequently, I turned to Python for testing until recently, when I discovered that MQL5 libraries now include all necessary components for strategy development and backtesting.

Pair trading shows promise, but several factors must be considered, such as analysis timeframe, candle window, and entry rules. Despite extensive efforts, crafting a robust strategy remains challenging. Nevertheless, I share MQL5 links containing essential libraries for native development in MetaTrader, fostering collaborative idea exploration.

In my analysis, I employ 288 five-minute candles, with a half-life of fewer than 24 candles. Additionally, I enforce an ADF of less than 0.05 on the spread (OLS residual). Entry conditions are met when observing a Z-score exceeding or falling below 2.

To solidify the strategy, further considerations are essential. Identifying pairs with the highest correlation within the chosen candle window is crucial. For instance, analyzing correlations within each candle, using a 288-candle lookback, helps identify pairs with correlations exceeding 80% most frequently. It's also valuable to assess which pairs consistently maintain an ADF below 0.05 over time.

Exploring optimal timeframes and stable windows is imperative. Transitioning to 1440 five-minute candles (1 week of trading) aims to enhance stationarity in entries and secure profit targets. However, resource constraints arise due to the strategy's computational demands.

Sharing this information aims to spark collaborative exploration. If you have insights, tested patterns, or calculations, we can review them. I have the necessary Python and MQL5 code for configuring rules and conducting tests. However, each day of backtesting currently takes approximately four hours to simulate.

Pair trading presents a compelling opportunity, yet refining a robust strategy demands meticulous analysis and collaboration. By leveraging Python and MQL5 resources, we can collectively explore and enhance pair trading methodologies.

For those interested, here are the links to the MQL5 articles containing the libraries utilized in this code:

1. Augmented Dickey Fuller test in MQL5
2. Implementing the Generalized Hurst Exponent and the Variance Ratio test in MQL5 - MQL5 Articles