Why Stock Price Levels and Returns Raise Different Regression Issues

Summary

The document raises a modeling question from a course example that uses principal component and factor analysis to predict stock prices. It reports the course author’s claim that regression should use returns rather than price levels, linking that recommendation to stationarity and trending behavior. The post asks for intuition behind the claim but provides no answer, supporting analysis, or empirical evidence.

The question highlights an important distinction in financial time series: price levels and returns have different statistical properties, and regression assumptions need to be considered when choosing a target and predictors. However, the premise as stated is unreliable: stock prices are not generally stationary, and regression does not universally require nonstationary or trending data. The document therefore serves as a prompt to examine stationarity and spurious relationships, rather than as a tutorial that resolves them. It does not specify a stock sample, model, test, or forecast result, so no conclusion about predictive performance can be drawn from it.

Key ideas

• The post asks why a forecasting model might use returns instead of stock price levels.
• It reports a course claim connecting regression to stationarity but supplies no explanation or evidence.
• Stock prices are not generally stationary, so the premise should be checked rather than accepted.
• The choice of target should account for the time-series properties of both target and predictors.

Tags

# Why Regression should only be done on Non-Stationary data points?


# Why Regression should only be done on Non-Stationary data points?












I am working through a course on PCA and Factor analysis, where the example is to perform regression on stock prices, with an objective to predict the stock prices.

The author claims, that we need to predict 'Returns' instead of 'Prices', as Prices are Stationary, and Regression always needs to be performed on NonStationary or Trending Data.

The explanation of above is out of the scope of the course.

Can anyone please share an intuition why does the said argument hold true?

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.