Elliott wave theory
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The Elliott wave theory is the basis of a technical analysis technique for predicting the behavior of the stock market, invented by R. N. Elliott in 1939. It is based on the belief that markets exhibit well-defined wave patterns that can be used to predict market direction, specifically that stock prices are governed by cycles which adhere to the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, etc.
It gives as the reason for this that the stock market, acting as a meter for mob psychology, displays many of the same geometric features as other organic structures. The Fibonacci sequence, which approaches the number Phi when represented as a ratio, can be seen in naturally occurring structures such as conch shells, flower petals, and even the joints of our fingers and arms. Proponents of the Elliott wave theory claim, and attempt to show, that the pattern is exhibited repeatedly in past market price patterns, and that the fractal nature of such patterns creates a repetition of them on varying levels of order and magnitude.
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Criticism
The theory is far from universally accepted. Critics deride it as being too vague to be useful, since there is not always a clear definition of when a wave starts or ends, and prone to subjective revision. Some critics have gone so far as to call it a borderline fraud, useful only for selling information to naive investors.
One major complaint is that if the theory is true, widespread knowledge of its patterns would lead so many investors to "bet" with it that the patterns would be altered, rendering it useless. This is a criticism that can be levelled against any predictive method based on public, market-wide data.
Specifics of the theory
According to the Elliott wave theory, markets move in a predetermined number of waves up and down. Specifically, markets move in five waves up and three waves down and price charts have a self-similar fractal geometry. This is true for bull markets. Waves 1, 3, and 5 are called impulse waves, and subdivide 1, 2, 3, 4, 5. Waves 2 and 4 are corrective waves, and subdivide a, b, c. In a bear market, the pattern is reversed, five waves down and three up.
References
"The Elliott Wave Principle" by Frost & Prechter. Published by New Classics Library P.O. Box 1618 Gainsville Georgia 30503.