Once in a while I see the golden ratio / Fibonacci numbers appears in the construction of technical indicators. (More specifically about Fibonnaci retracements, see here for example - "For unknown reasons, these Fibonacci ratios seem to play a role in the stock market, just as they do in nature."). I am not here to discuss the usefulness of TA as a whole. But I am curious about that specific definition / usage.
Is there any theoretical basis that would justify the usage of the golden ratio / Fibonnaci numbers when looking at stock price patterns ?