If you pick two consecutive numbers on the Fibonacci sequence, square both, subtract the smaller from the larger, and then subtract the product of those numbers, the answer seems to always be + or -1. Does this hold true forever? Why?
Was screwing around and noticed this pattern, and find it curious.
Haven't had much success testing beyond F40 (102334155) because of floating point errors, but it holds until then. This seems really counterintuitive to me, but is there an obvious explanation for why this pattern exists? Edit: TIL of Cassini's / Simson's Identity, which with some easy rearranging and substituting can be converted into the equation I listed. The pattern does hold, and points me in a direction to keep looking for understanding why.
A proposed alternative approach to Fibonacci retracements
In the book The Art and Science of Technical Analysis, we can find a statistical analysis performed by the author on the validity of Fibonacci ratios in financial markets. I won’t get into details because it’s long and the research is freely available on his website. Long story short, the findings were pretty conclusive:
Fibonacci ratios do not provide an edge.
The vast majority of trends retrace to around 50% of the setup leg, with a standard deviation of about 20%.
I currently trade the bands system shared a couple of months ago. I backtested it and it shows a clear edge, but since it incorporates the Fibonacci ratios for entries, targets and stops, the mentioned research occasionally pops back in my mind and makes me wonder whether I just got lucky and should review. And so I started to think. After a bit, I reached a conclusion that satisfied me. The spark was the second conclusion of the research, the fact that good trends are statistically likely to retrace in the general area of 50%. Ok, so, what does “general area” means? Would a buffer of 10% be enough? If we do this, we would have an interval composed by three retracements:
If we compare the upper and lower values to the closest Fibonacci ratio, we get the following.
| 0.60 - 0.618 | = 1.8%
| 0.40 - 0.382 | = 1.8%
(I know it’s an obvious calculation but I just want to make my point clear) In other words, Fibonacci numbers are pretty close to what we can realistically assume to be a “general” area around the statistically expected retracement level of 50%. The difference is just 1.8%. I should also note that the 61.8 and the 38.2 are the most widely used ratios as far as I am aware. Considering that most people who use Fibonacci ratios will consider a level respected even if price goes slightly above or below it, it sounds fair to accept 1.8% as an irrelevant difference. To put things into other terms, what I am saying is that if we took the track records of all the trades taken by traders who use Fibonacci ratios in a non purely mechanical way, and we shifted their ratios up or down by 1.8%, I am willing to bet their performance would be virtually identical. What does this suggest to me? It makes me think that, maybe, their edge is not in the Fibonacci ratios. Maybe the specific ratios have no significance at all. It seems to me that the idea of expecting a retracement in the area around half way into the impulse leg is what actually drives their performance - with a margin of error of 1.8%. Maybe the edge of the strategy I trade would not change if, instead of entering on the 23.6% and the 38.2% retracements as I do now, I placed my limit orders on the 25% and 40% retracements instead. I will do further testing.
Can somebody please explain to me simply (like I’m 5) what this means? I can’t for the love of god understand what babypips is talking about. I know what the golden ratio is and have for a while but I’m not at all understanding how this applies to trading with how babypips is explaining it.
The Fibonacci sequence is one of the most famous formulas in mathematics. Each number in the sequence is the sum of the two numbers that precede it. Fibonacci numbers and lines are technical tools for traders based on a mathematical sequence developed by an Italian mathematician. These numbers help establish where support, resistance, and ... Fibonacci, medieval Italian mathematician who wrote Liber abaci (1202; ‘Book of the Abacus’), the first European work on Indian and Arabian mathematics. Little is known about Fibonacci’s life. His name is known to modern mathematicians mainly because of the Fibonacci sequence. Fibonacci refers to the sequence of numbers made famous by thirteenth-century mathematician Leonardo Pisano, who presented and explained the solution to an algebraic math problem in his book Liber Abaci (1228). The Fibonacci sequence and the ratios of its sequential numbers have been discovered to be pervasive throughout nature, art, music, biology, and other disciplines. Fibonacci was not the first to know about the sequence, it was known in India hundreds of years before! About Fibonacci The Man. His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy. "Fibonacci" was his nickname, which roughly means "Son of Bonacci".
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