This paper empirically investigates the predictive power of Fibonacci retracement levels as indicators of support and resistance over the period 2015-03-31 to 2025-03-31. We construct a continuous Fibonacci indicator by algorithmically mapping local price ex-trema using kernel regression and detection of local extremas, normalizing the price po-sition relative to the {0 %, 38.2 %, 50 %, 61.8 %, 100 %} retracement levels, and smooth-ing with an exponential moving average. First, we estimate next-day log returns on lagged Fibonacci values using OLS regressions with Newey–West–adjusted standard errors. Second, we model conditional volatility in a GARCH(1,1) framework with the squared Fibonacci indicator as an exogenous term. Critical values are calibrated via block-boot-strap to control for autocorrelation and heteroskedasticity under the null of random walk. Results show a consistently negative and significant relationship between proximity to support levels and subsequent returns, and a positive, significant effect on volatility con-traction at Fibonacci levels. These findings support the use of Fibonacci retracements in technical analysis while acknowledging variation across markets.