One of the most important steps in developing a profitable statistical arbitrage trading strategy is choosing the right pairs of stocks to trade. This can be a difficult and time-consuming process, but it is essential in order to find pairs that are likely to produce profitable results.
There are a number of different methods that can be used to find potential pairs of stocks for statistical arbitrage. One common method is to use a stock screener to find stocks that are highly correlated. This can be done by looking for stocks that have a high positive correlation coefficient. One can also look at the cointegration with the goal of finding stationary spread time series.
Reference  looked at statistical arbitrage in the foreign exchange market and proposed an approach that involves 3 currency pairs. Basically, it attempted to use a relaxed form of the triangular arbitrage rule in order to construct a basket of currency pairs for trading that are highly cointegrated.
This paper presents an application of statistical arbitrage to foreign exchange markets and specifically on instruments that obey a triangle rule/law. These instruments have a long-term cointegration relationship which leads to the mean-reversion behaviour evident in their data. Metatrader 4 is used to develop an indicator which in turn is used to gather and process price data and inform an investor on when and how to invest in a particular combination of three instruments obeying the triangle rule. That is, a simple strategy is outlined and its long-term profitability is demonstrated using expectation value under some mild assumption of stability of cointegration model parameters.
In short, the author claimed that by using a relaxed form of the triangular arbitrage rule a profitable trading strategy can be developed.
We find the idea plausible, but given that the currency basket contains many instruments, we believe that commissions will eat away any potential profit.
Let us know what you think in the comments below.
 NJ. Matjelo, Triangular Statistical Arbitrage in Foreign Exchange Market, IJISET – International Journal of Innovative Science, Engineering & Technology, Vol. 09 Issue 03, March 2022
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