Japanese Correlation Coefficient

Introduction

This indicator was asked and named by a trading meetup participant in Sevilla. The original question was "How to estimate the correlation between the price and a line as easy as possible", a question who got little attention. I previously proposed a correlation estimate using a modification of the standard score (see at the end of the post) for the estimation of a Savitzky-Golay moving average (LSMA) of order 1, however something faster could maybe be done and this is why i accepted the challenge.

Japanese Correlation

Correlation is defined as the linear relationship between two variables x and y, if x and y follow the same direction then the correlation increase else decrease. The correlation coefficient is always equal or below 1 and equal or above -1, it also have to be taken into account that this coefficient is quite smooth. Smoothing is not a problem, scaling however require more attention, high price > closing price > low price, therefore scaling can be done. First we smooth the closing/high/low price with a simple moving average of period p/2, then we take the difference of the smoothed close with the smoothed close p/2 bars back, this result is then divided by the difference between the highest smoothed high's with the lowest smoothed low's over period p/2.

Since we use information provided by candlesticks (close/high/low) i have been asked to publish this estimator with the name Japanese correlation coefficient, this name don't imply the use of data from Japanese markets, "Japanese" is used because of the candlestick method coming from Japan.

Comparison

I compare this estimation with the correlation coefficient provided in pinescript by the correlation function.


The estimation in orange with the original correlation coefficient using n as independent variable in blue with both length = 50.


comparison with length = 200.

Conclusion

I have shown that it is possible to roughly estimate the correlation coefficient between price and a linear function by using different price information. Correlation can be further estimated by using homogeneous bridge OHLC volatility estimators thus making able the use of different independent variables. I really hope you like this indicator and thanks to the meetup participant asking the question, i had a lot of fun making the indicator.

An alternative method