Stochastic Models and Dynamical Views of Financial Time Series

Summary

The document raises a conceptual question about whether financial time series should be viewed as stochastic processes or as dynamical systems shaped by interacting, changing influences. It uses reinforcement learning as an example: a Markov Decision Process represents uncertain transitions and is commonly used to model sequential decisions. The author contrasts that modeling choice with the intuition that prices arise from complex historical and present-day factors, rather than from pure randomness.

The text asks whether practical complexity makes a stochastic model a useful approximation, and whether that framing misunderstands financial prices. It does not provide an answer, empirical comparison, or formal model, so it serves as a prompt for distinguishing a model’s probabilistic representation from claims about the underlying market’s true nature. Its scope is broad and exploratory; it does not establish that prices are deterministic or assess when an MDP is appropriate for trading.

Key ideas

• The document contrasts stochastic descriptions with dynamical explanations of financial price behavior.
• An MDP represents uncertain state transitions and can frame sequential decision problems.
• A probabilistic model can be used as a practical representation without proving that the market is fundamentally random.
• The document poses the modeling question but provides no empirical resolution.

Tags

# Financial Time-Series: Stochastic or Dynamic?


# Financial Time-Series: Stochastic or Dynamic?












I have learned how some methods of constructing predictive models of financial time-series involves assumptions of stochasticity. For example, reinforcement learning utilizes the Markov Decision Process (MDP) which is meant to model a stochastic system.

However, from my perspective, financial time-series are more accurately defined as dynamical systems in that they are the product of complex interplaying factors from past and present that are constantly changing the system.

This is because, in reality, the stock price isn't truly random (stochastic), its price fluctuations are just so complex that it is easier to chalk it up to randomness (in my opinion).

Is the reason we can use MDP because the financial time-series is so complex that it may as well be a stochastic system?

Is there something else that I am misunderstanding?

Thank you!

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