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Limits of Price-Only Forecasting and the Role of Factors

Article Quant Q&A · Author: PlatinumMaths
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Summary

The document concerns choosing a mathematical topic for stock price forecasting and discusses geometric Brownian motion, differential equations, neural networks, ARIMA models, adaptive filtering, and factor methods. Its answer argues that neural networks trained only on historical prices may overfit and fail to predict unseen data. It suggests that neural networks may be more useful when they combine prices with explanatory factors, giving weather, seasonality, economic output, and income as examples. ARIMA and Kalman filtering are named as alternative approaches, while a connection between the Black–Scholes equation and heat diffusion is briefly mentioned.

The response offers opinions rather than empirical comparisons, and gives no data, evaluation design, or quantitative results to support its claims. It does not develop a geometric Brownian motion forecasting method or provide a usable trading strategy. Its central research caution is to assess out-of-sample performance and distinguish price-only prediction from models using external factors; its broad claims should be treated as hypotheses to investigate, not settled evidence.

Key ideas

  • The response warns that neural networks fitted to price histories can overfit and generalize poorly.
  • It proposes external explanatory factors as possible inputs for forecasting models.
  • ARIMA and Kalman filtering are mentioned as alternatives to neural networks for price-only modeling.
  • The Black–Scholes equation is linked briefly to a heat diffusion equation.
  • The document presents no empirical test to validate its forecasting claims.

Tags

EquitiesMachine learningStatisticsFactor investing
Full text
# Using geometric brownian motion for stock price forecasting


# Using geometric brownian motion for stock price forecasting












I am doing a dissertation in finance on a maths degree. I wanted to forecast stock prices using artifcial neural networks but none of my tutors are able to supervise so I'm having to do something else.

I would like to do something similar, something that I could also use for my own personal use. If possible, please suggest some mathematical models.

Anything cool that I could do with a differential equation? I am open to other topics too, but something with which I could actually make some money. Or atleast aid my investment decision making with.

## Answer by Con Fluentsy (score 1)

https://quant.stackexchange.com/a/60002

The reasons why your Professors were unaware of neural networks in forecasting stock prices is because, if you intend to model stock prices alone, it does not work, hence nothing has surpassed either ARIMA modelling or adaptive filtering, eg. Kalman filters. The reason why NN does not work is because they can be easily trained to perfectly fit the training data, but they have virtually no forward predictability on test data, as they by the nature of the method overfit a model. However, NN can be very accurate in forecasting prices using factor methods, eg. linking ice cream stocks to such things as daily temperature, season, GDP, Disposable income, etc. But not on prices alone. It is hard to see how you have got to do a Ph.D. when fundamentally do not understand that a differential equation gives either an unstable or stable solution( I am making an assumption here, I could be incorrect, you may be aware), given that the BS formula can be derived by a differential equation analogous to Einstein's heat diffusion equation, it is possible a prediction within a range is possible, it is in the realm of econophysics, which I will leave for others.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.