The Elliot Wave Theory states basically that a rising stock will rise in a 5 step wave. Step 1 - up, Step 2 - down but not to the start of step 1, Step 3 - up (passing the previous high), Step 4 down (but not to the start of step 3) and step 5 up (surpassing previous high).
It also states that a falling stock will move in a 3 step wave (down, up, down).
Fibonacci analysis is based on the principle that stock price will move from price a - b and then retrace 38%,50% or 62% before continuing the trend set by the movement from a-b