: Theoretical justification for technical analysis What are the theoretical justifications for the operation of trading algorithms based on technical analysis using different indicators such as rsi, stochastic, macd, etc.?

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Individual securities as well as the market have a periodicity that varies between high and low prices along with periods of range trading. If the period that you select for your indictor matches the periodicity of your security, the indicator works.
What does the above mean? Pick a security, an indicator as well as an individual bar time (minute, hourly, daily data, whatever) and optimize across those time periods. Let's say it's daily data and you back tested 5 days through 25 days. One of those time periods is going to produce the best result and some are likely perform poorly.
Now suppose that you have identified this ideal time period. Break you data into some number of extended time periods, say 5 years of data and now test one year at a time. You'll find that in some years it did well and in other years, not as well.
Now test that ideal time period on another security. Rut roh, not likely to work because this other security has its own unique ideal indicator length because each security has its own cyclical character.
So what's the point? The ideal time period for each indicator is only known in hindsight.
This is an oversimplification of technical analysis which is more complex than this. I'm just offering an explanation as to why it's not going to work at its most basic level. The proponents of this will argue the case that it is effective but they tend to be purveyors of fee based software, data for such software, newsletters, stock picking services, etc. If it really did work by just implementing an algorithm, why are these purveyors selling the dream rather than mortgaging the farm and trading their way to untold wealth instead of hawking such services?
Yes, you can find an edge in the market and make good money (think Michael Burry in The Big Short or Universa Fund making 4,000% from the market collapse in March). Yes, algorithms can be used to exploit market inefficiencies (think high frequency trading). But no, you're not going to take some combination of canned or even custom indicators, write an algorithm and print money. If that could be done, trading desks, hedge funds et al would be doing it and none would ever lose money. None would ever take the other side of the trade. And the next time someone tries to convince you otherwise, ask them to post their new picks in real time. Seeing is believing.