why are such methods not employed by more frequently by
economists/econometricians?
Because the so-called technical analysis ("TA") is overly simplistic and devoid of mathematical (or at least rational) basis.
The application of algebra, probability, time series, and other tools & disciplines does not guarantee accuracy of forecast, but at least that application provides a more robust framework with which to model financial data than what is achievable through TA. Just to mention one example, TA does not address arbitrage opportunities, which is a useful and consistent approach to pricing financial instruments.
I noticed though the methods were simple and required little knowledge
of statistics, they worked very well. They call these methods as a
part of trend analysis.
There is a false sense of accuracy surrounding TA. Materials that teach or promote TA obviously will present instances where --in hindsight-- the method appears to work. But nothing in TA predicts, models, or at least explains the price trajectory of a financial instrument (let alone its timing).
I think that if/when TA supposedly "works", it is only because of a kind of self-reinforcing feedback: TA "indoctrination" inadvertently prompts TA adepts to reinforce that, say, a price-band (or however it is called) is about to be broken because the price of the stock has touched its limit twice. Thus, TA-based traders react by performing certain transactions expecting to profit from the supposedly imminent direction of the stock.
