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Subwaves of an impulse

I opportunistically selected the advance from September 18, 1985 to January 7, 1986 for its distinctive shape. Within this wave, a 10-day moving average distinguished nine subwaves with the following advances or declines:

The resulting advance/decline ratios of upwaves to subsequent downwaves were 2.534,2.982,5.903 and 2.758, respectively. The number of advancing days from September 18, 1985 to January 7,1986 is 50 and the number of declining days is 26, giving a ratio of 1.923. The ratio of total advances to net advances is 1.338. From these, I can deduce no connection to Fibonacci numbers or the Golden Ratio.

The period from June 20,1985 to September 18,1985 also was selected opportunistically as a typical neutral period consisting of one upwave and one downwave. During this period there were 35 advancing and 26 declining days, giving a ratio of 1.346. The average advance was 4.606 points and the average decline 6.108, giving a ratio of 0.754.

What seems like a downtrend to one observer is just a minor

correction in an overall uptrend to another.

Conclusion

In my findings, none of the ratios examined for the waves defined by moving average crossovers have a mean of 1.618. This was clearly shown for waves defined by 10-day moving averages.

While the data does not allow me to reject the null-hypothesis that the ratios are equal to 1.618 for waves defined by 20- or 30-day moving averages (with one exception), this does not mean the null-hypotheses are accepted.

Rather, the assumed "self-similarity" between waves of different degrees suggests that the same results should be obtained regardless of the degree of the waves. Therefore, the inability to reject the hypothesis is most likely due to the small sample size. In any case, all the ratios, for all moving average cycle lengths, show a large measure of dispersion with standard deviations on the order of the respective means, suggesting that the cycle lengths are poorly estimated.

There are many reasons why a Fibonacci relationship might not show up in an investigation of this kind, even if some such relationship exists. For example, the method of determining up- and downwaves using moving averages, while objective, does not allow for any "internal" wave structure, such as an "irregular correction" to an upwave, which might extend to a new high, although it properly should be counted as a downwave. Or, possibly, I looked at the wrong ratios, or perhaps the 182 days of data were insufficient for any kind of consistency to become apparent.

Nevertheless, I believe that if there were an underlying relationship between Fibonacci ratios and stock prices, some evidence would have turned up in the data studies I performed. And so, I believe the reason we find a great variation in advance/decline ratios rather than some consistent ratio is that stock market trends can occur in any degree of intensity or steepness, and this would naturally be reflected in the ratios that were examined.