Fibonacci analysis applies mathematical ratios derived from the Fibonacci number sequence (0.236, 0.382, 0.618, 0.786) to financial market analysis. These ratios are used to identify potential support and resistance levels, price targets, and reversal points based on the theory that markets move in predictable proportional relationships. Fibonacci retracements and extensions are widely used technical analysis tools.

Traders use Fibonacci retracements to identify potential buying opportunities during pullbacks in uptrends or selling opportunities during rallies in downtrends. The most significant Fibonacci levels are 38.2%, 50%, and 61.8% retracements, which often act as support or resistance. While not infallible, Fibonacci levels gain significance when they align with other technical indicators or fundamental factors.

Real-world example: After Apple stock rallies from $100 to $150, traders watch the 61.8% Fibonacci retracement level at $119 as potential support for establishing long positions, expecting buying interest at this mathematically significant level.