# Cointegration Matrix (FX)

This indicator plots a cointegration matrix for pairings of all 28 major forex pairs. The matrix is populated with ADF t-stats (from an ADF-test with 1 lag). An ADF-test (Augmented Dickey-Fuller test) tests the null hypothesis that an AR process has a unit root. If rejected, the alternative hypothesis is usually that the AR process is either stationary or trend-stationary.

Technically what we're doing is running an ADF-test on the residuals (spread) of each pairing (i.e. a cointegration test). So we're testing if there is a unit root in the spread between the two assets of a pairing. A unit root being present in the spread essentially means the spread varies randomly over time, and any mean reversion in the spread is very hard to predict, or may never happen. If there is no evidence of a unit root, the spread (distance between the assets) should remain more or less constant over time, or rise/fall in close to the same rate over time (if it can be modelled as an AR process). The more negative the number, the stronger the rejection of the idea that the spread has a unit root. So in statistics we choose a critical value that corresponds to a confidence level of the test. In this case, -3.238 equals a confidence level of 90%, -3.589 equals a confidence level of 95% and -4.375 equals a confidence level of 99%. So the colors are based on the confidence level of the test statistic (the t-stat, i.e. the number of the pairing in the matrix). So if the number is greater than -3.238 it is green, if it's between -3.238 and -3.589 it's yellow, if it's between -3.589 and -4.375 it's orange , and if its lower than -4.375 it's red.

There are multiple ways to interpret the results. A strong rejection of the presence of a unit root (i.e. a value of -4.375 or below) is not a guarantee that there is no unit root, or that any of the two alternative hypotheses (that the spread is stationary or trend-stationary) are correct. It only means that in 99% of the cases, if the spread is an AR process, the test is right, and there is no unit root in the spread. Therefore, the results of this test is no guarantee that the result proves one of the alternative solutions. Green therefore means that a unit root cannot be ruled out (which can be interpreted as "the two forex pairs probably don't move together over time"), and red means that a unit root is likely not present (which can be interpreted as "the two forex pairs may move together over time").

One possible way to use this indicator is to make sure you don't trade two pairs that move together at the same time. So basically the idea is that if you already have a trade open in one of the currency pairs of the pairing, only enter a trade in the other currency pair of that pairing if the color is green, or you may be doubling your risk.

NOTE: The indicator can take a while to load since it is loading data from 28 pairs and calculating the ADF t-stat for 756 pairings.

• Added the option to change the size of the text, so that the matrix can fit in smaller monitors.
• Added the option to change the text color, to accomodate people who aren't using the dark color theme in TradingView.