Evaluating Signals Beyond Correlation and Linear Regression
Summary
The document describes a simple monthly trading rule that takes a long position when a signal is positive and a short position when it is negative, with trades timed around adjacent observations. Applied to different signal and asset pairs, the strategy appears profitable for some and not others. The author seeks a way to explain this variation or identify characteristics of promising pairs, while recognizing that observed profits alone do not establish causality.
Rank and linear correlations with prices or returns are reported as low for the profitable pairs, and regression yields insignificant slopes and low explanatory power. The document presents this as an open research question rather than a tested solution. It gives no evidence about out-of-sample performance, transaction costs, timing bias, or which alternative measures would distinguish reliable relationships from chance findings.
Key ideas
- A simple sign-based rule can produce different observed outcomes across signal and asset pairs.
- Low correlation and weak linear regression results do not explain the apparent profitable pairs.
- Observed cumulative profit alone does not establish a causal or robust signal relationship.
- The document raises the need for further criteria but does not provide a validated alternative.
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Full text
# Account for empirical relationship between signal and market data
# Account for empirical relationship between signal and market data
I have two monthly time series : one is a 'signal', on which I will base my decision to buy or short-sell, and the second one is the time serie of a given asset's price.
I have implemented this extremely naive algorithm : if the signal at time t is positive, buy at t-1, sell at t, if it is negative, short at t-1, buy at t. Testing several (signal, asset) pairs, I find that for some of them I make significant cumulative profit over the years, and for some other, I don't.
So I want to explain why this works for some pairs and not for others (or, instead of causality, find a criteria or a quantity that would be characteristic of "good pairs"). Purely investment-wise, it might (but not more than "might") be enough, but I can't be satisfied with it, and it's not rigorous.
So far, I have (with Python/pandas):
- computed the correlation (Spearman, Kendall and Pearson) between the signal time serie and the asset price / returns, but the results are low for the good pairs
- tried to perform a linear regression the returns against the signal, but the $\beta$ are insignificants and $R^{2}$ very low, which points (as far as I understand) to at least no linear relationship between the two time series
I would like to know what other leads to explore (I gladly accept books/articles references as well, if this is an extensively discussed question !)Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.