Correlation simply means "to move together". Pearson's correlation or simply correlation assumes linearity. I'm not really sure on the value of correlation. But, traders have cited some ways they have used correlation:

1. Correlation can be used for confirmation. For example, if two markets are correlated and they both go up or down then one might view it as a real move whereas if only one goes up then one might view the one that goes up as an opportunity to short. This is often used when thinking of spread trading or spread ideas. The problem is markets are arbitraged heavily.

2. Sometimes correlation is used to identify potentially predictive variables. For example, if I have a variable Z that is correlated with price then if I can predict Z then I can predict price. Of course, it assumes Z is easier to predict then price.

3. If we allow ourselves to look at correlation of lead or lags in time then it looks like prediction. X lag 1 correlated with a rise in price is stating X is predictive.

4. Correlation is often used in spread trading. If the two instruments are correlated and if the spread is wide: the idea is to buy the under-priced and sell the over priced. However, correlations in markets can break down.

5. There is surely some important relationship between linear regression and correlation.

So if i'm using a correlation study to compare the ES and the NQ as a means to use the market internals that are geared to the NQ, would that be a false derivation? Should i include another brand of market internals coupled with this correlation study?

@sholcombe4 Sorry I am not sure whether or not I understand your question. Remember, correlation just measures the tendency of two things to move together. If you want to use some data in your trading, using correlation as a means to test if it makes sense to use the data would make sense.

As for ES/NQ, if you wanted to spread trade these you would want to look at the correlation and cointegration to see how they are related. A widening spread indicates sentiment that the market anticipates one market to outperform/under-perform the other. Statistically, if the markets are highly correlated (really co-integrated) it might also suggest an arbitrage opportunity with a high probability of the spread narrowing.

If you are using the "confirmation" thesis/example then yes you would want to know if the time series are correlated, this tells you if it make sense to use the data.

Right regarding market internals, you might want to measure whether or not the market internals are correlated with price change before using them. However, whether or not it makes sense to use NQ market internals for ES market: we know the correlations will be less using NQ internals for ES data right off the bat. So, the rational thesis must be the ES internals will be better for ES market vs using the NQ internals for ES market. Why? Because the internals measure the subcontinents of the index. However, and this is where things get complex -- if you have a complex non-linear model then you might derive some value even from weakly correlated data. As well, even very low R^2 scores on data can still be used to build profitable trading systems.

I mean think about it this way, it is highly likely that volume on NQ and volume on ES are highly correlated. However, if you want to know the volume for the given instrument, it is available, we know that the volume for ES will move with volume for ES 100% of the time. So, we know that even if the NQ volume is correlated, it will never be as useful as ES volume (if volume is even useful) with the caveat/exception if we are somehow able to combine them.

Now, let me give an example where it can make sense to use correlation. Let's take an instrument like BTCUSD (but also applies to stocks) that trade on many exchanges. There are internal/intrinsic factors that will affect market maker pricing and external/extrinsic factors. Intrinsic factors might be a market makers risk exposure, probability or tendency to try gaming (competition), and net exposure.

Let's imagine the GDAX market maker has too much net long exposure and thus pull some resting limit buy orders from the book. This makes it easy for a low volume of selling to dip the price. If we know that the dip in price is only because of intrinsic factor concerning the market maker (and/or the participant) then we can anticipate it is more likely to be a good dip to buy versus if there was a trend developing or if all exchanges were dipping in price.

In this case, we'd like to use correlation to know if the move is real. In order to understand this, it helps to imagine/understand the use case of the alternative. Imagine if some sort of negative news comes out, maybe something about new regulations. We might imagine that participants will sell on all the exchanges. In this case, we anticipate to see the price dip (move together) on all the exchanges. This change in price is more likely to represent the consensus of the market participants and not to be a good dip to buy for an immediate profit.

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A similar concept is explained in the webinar above

Correlation in autotrading can be used to increase stability of a portfolio containing intraday strategies even on the same instrument depending on the period choosen for which they are studied it can be based on hourly , daily,weekly or monthly profit/loss in trades taken. I just use correlation of loss on monthly basis. If one strategy is loosing i want the other one to be winning. When both are winning it is great but i do not want them to be loosing at the same time if possible.