Markov Assumptions, Hidden Markov Models, and Price Predictability
Summary
The note examines why Hidden Markov Models are used for financial prices despite their first-order Markov assumption: future states depend on the present state, rather than directly on the full path of prior observations. It also asks whether technical patterns such as support, resistance, trends, and candlestick formations conflict with that assumption or are incorporated during Baum–Welch training.
The response distinguishes perceived chart patterns from rules that have been defined precisely enough for statistical testing. It warns that flexible pattern interpretation and repeated strategy searches can produce apparent successes by chance. The author argues that market dynamics are unlikely to be exactly Markovian, but that trading on exploitable dependencies may push prices toward Markov-like behavior. The proposed strong prior in favor of Markov dynamics is a modeling judgment, not an empirical demonstration that all market prices satisfy the property.
Key ideas
- A first-order Markov model makes the present state sufficient for describing the distribution of future states.
- Chart patterns only provide testable evidence when translated into explicit rules.
- Flexible pattern selection and extensive backtesting can produce misleading apparent performance.
- Market dynamics may deviate from the Markov property even if competition reduces persistent predictability.
- Treating Markov behavior as a strong prior is a modeling stance rather than proof of exact Markov dynamics.
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Full text
# Why do we make the Markov assumption on financial markets? # Why do we make the Markov assumption on financial markets? Why are Hidden Markov Models (HMM) a good fit to describe the behaviour of the prices of financial assets, when these models require that the underlying stochastic process satisfies the first-order Markov property? According to such property, the probability of future events it's only determined by the current state of things. However it's commonly known among technical traders that trend lines, support/resistance levels, previous candels formations, etc. play a big role in determining prices. What am I missing? Are these factors implicitly taken into account when the HMM is trained through the Baum-Welch algorithm? ## Answer by Stéphane (score 3) https://quant.stackexchange.com/a/54008 The markov property imposes a form of unpredictability on price dynamics within financial models. As you noted, if this was exactly true, technical traders would effectively be wasting their time. Now, there is a bit of a problem in what you wrote about technical traders. They believe that some price patterns can predict future stock prices, but this is very different from having established this predictability on sound statistical ground. My experience talking with people who engage in analyzing price patterns using concepts such as resistence and support levels, candle stick patterns, trend lines, etc. is that they are using a very fuzzy rule. If you ask them to make those rules explicit, they would all fail to do it which means by definition that they are unable to run backtests. With enough randomness and enough such traders, even in a Markovian world, a handful would be bound to be regarded as geniuses just as running a gazillion backtests on a limited amount of data is bound to turn up arbitrarily high Sharp ratios on a trading strategy, again, even in a Markovian world. So, who's right? Well, I strongly doubt that financial markets would organize themselves to magically produce exactly Markovian dynamics. On the other hand, people trying to take advantage of non-Markovian dynamics would presumably push prices most of the time towards being more Markovian. That point is precisely why I think your prior should always be that price dynamics obey the Markov property -- in fact, I think that should be a pretty strong prior.
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