Let ( r 1, …, r n) be a contracting ratio list. If S ⊆ X and d ∈ [0, ∞), the d dimensional Hausdorff content of S is defined byĬ H d ( S ) : = i n f Ī finite collection of real numbers ( r 1, …, r n) is called a contracting ratio list if Section snippets Hausdorff dimension of Elliott waves Section 4 is the application of Elliott waves and the corresponding fractional Brownian motion to Japan Nikkei 225 index together with some simulation results. Section 3 gives the linkage between Elliott wave and fractional Brownian motion. The rest of the study is as follows: In Section 2 the Hausdorff dimension of Elliott wave is computed. Elliott waves have fractal nature however, similarity patterns are not identical like Koch snowflake. Wave C is the realization of the bear market.Īnother important characteristic of Elliott wave is its self-similar patterns. Wave B is the retracement of wave A, which is regarded as the continuation of the upward trend in a wrong manner. Most investors regard the down movement as a retracement as in wave 2 or wave 4. As in the case of wave 1 its inception is not obvious since news are positive. Wave A is the beginning of downward trend. Wave 5 is the final piece of the bull market. Wave 4 is another corrective move where the level of retracement is lower than 38,2%. Wave 3 is the most powerful and largest wave and usually goes beyond wave 1 by a ratio of 1,618: 1. However, prices do not retrace more than 61,8% which comes from a Fibonacci relation. Second wave is the retracement of wave 1. Economy looks bad and analysts are bearish. (for details see, , )įirst wave is the beginning of the upward trend which usually hard to observe at its early stages. These waves have special rules and restrictions as described below and shown in Fig. 1. This is the beginning a downward movement with some upward corrections. Moreover, after a peak, investors become pessimistic and the trend is reversed. According to this model, once stock prices are on an increasing trend, they are followed by some corrective patterns called retracements. Elliott in the sense that investors become bullish and bearish according to certain cycles. This phenomenon became a yardstick for R. Human mind tends to perceive movements in a rhythmical fashion.
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