How to turn a contemporaneous regression into a predictive trading signal

General
1

Course Name: Financial Time Series Analysis for Trading, Section No: 9, Unit No: 6, Unit type: Notebook

In the notebook we estimate the following regression:

JPM = -18.11 + 1.55 * BAC + 1.26 * C

I have two questions regarding how this could be used in practice.

1) Descriptive vs predictive regression

As written, the variables BAC and C appear to have the same timestamp as JPM, so the equation effectively looks like

JPM_t = -18.11 + 1.55 * BAC_t + 1.26 * C_t
​
This seems descriptive rather than predictive, since the explanatory variables use information from the same time step as the dependent variable.

For trading purposes, a predictive formulation would appear more useful, e.g.

JPM_t = -18.11 + 1.55 * BAC_{t-1} + 1.26 * C_{t-1}
​
How would one move from a contemporaneous (descriptive) regression to a predictive one?

Is there a more principled approach than simply lagging the explanatory variables?

2) Identifying lead–lag relationships

2.1
More generally, suppose we believe BAC helps predict JPM. What ensures that the relationship is stable over time and does not flip direction (e.g. JPM predicting BAC instead)?

How would we empirically determine which asset is leading and which is lagging?

2.2)
For example, if a stock trades simultaneously on two venues (say LSE and Chi-X), how could we determine whether price changes on one venue systematically lead price changes on the other?

Any pointers on techniques for analysing lead–lag relationships in financial time series would be appreciated.

2

Thanks Benjamin, good questions.

  1. In the notebook the regression uses prices at the same timestamp. The goal is mainly to show how multivariate regression captures co movement between assets. In practice this type of regression is often used in relative value or pairs trading where we estimate a relationship between assets and monitor the residual spread rather than trying to directly predict JPM.

If the goal is prediction, then using lagged variables such as BAC_{t-1} and C_{t-1} is a common approach. More systematic ways to model predictive relationships include VAR models or Granger causality tests, which allow the data to determine whether past values of one asset help explain another.

  1. To study which asset leads and which lags, common techniques include cross correlation of returns at different lags, Granger causality tests, or VAR models. For the example of the same stock trading on two venues, similar methods are used in market microstructure studies to see whether price changes on one venue tend to appear slightly earlier than on another.