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STATISTICS


Primary Bull Market Secondary Reaction

07/26/11 09:30:11 AM
by Alan R. Northam

Statistical analysis is used to help clarify the difference between a secondary reaction within an ongoing bull market or the establishment of a new bear market.

Security:   .DJI
Position:   N/A

The Dow theory recognized that during the course of a primary bull market, there are at least two secondary reactions. The theory states that these secondary reactions are necessary to keep excessive speculation in check. The theory states that a secondary reaction normally lasts from three weeks to as many months and retraces from one third to two thirds of the advance from the previous secondary reaction. The theory also warns students of the Dow theory not to put hard limits on the definition of a secondary reaction or they will be doomed to failure. The theory further states that secondary reactions are deceptive, as it is most difficult to distinguish a secondary reaction from the beginning of a new trend.

The latest secondary reaction in the Dow Jones Industrial Average (DJIA) began in late April 2011 and ran through late June, thus satisfying the time from for a secondary reaction. The reaction was also quite deep, moving below the low point of a minor reaction that ended in mid-April, and most likely satisfies the retracement requirement of a secondary reaction. The question becomes, "Is this a valid secondary reaction within a continuing bull market, or is it the beginning of a new bear market?" If it is a valid secondary reaction, then we must expect the Dow Jones Industrial Average (DJIA) to move higher. However, if this is the beginning of a new bear market, then we should not expect the DJIA to move higher than the high it made in late April.

To avoid trying to second-guess the Dow theory, one solution is to use statistical analysis and follow the results that it provides.

The bottom panel of Figure 1 shows the daily price bars of the DJIA. This panel shows the 50-day linear regression line (middle downsloping red line) along with its upper and lower three sigma channel lines. The linear regression line (the middle line) represents the slope of the secondary reaction and is often referred to as the linear regression trendline. The upper and lower three sigma channel lines represent the range in which price statistically moves 99.7% of the time. Once price moves outside the three sigma channel lines, a signal is given that there is a high probability a change in the direction of the trend lies ahead.

Note that in Figure 1, price has moved outside the upper three sigma channel line, signaling a high probability that the direction of the movement of price has now shifted from a downward movement to an upward movement. I have also added the upsloping 50-day linear regression line along with its upper and lower three sigma channel lines. As long as price remains above the downsloping red upper channel line, the upward direction in price should continue.

FIGURE 1: DJIA, DAILY. This chart shows the daily price chart of the Dow Jones Industrial Average, in the bottom panel along with the 50-day linear regression trendline and its upper and lower two sigma channel lines, the linear regression slope indicator in the top panel, the R-squared indicator in the second panel, and the relative standard error index (RSEI) in the third.
Graphic provided by: MetaStock.
 
The top panel of Figure 1 shows the linear regression slope indicator. When this indicator first crosses its zero line from below, it signals the beginning of a new intermediate-term upward rally, which is part of the composition of the primary bull market trend. As can be seen in the top panel of Figure 1, the linear regression slope indicator has recently moved above its zero line, marking the beginning of a new intermediate-term upward price rally.

The next window down from the top shows the R-squared indicator. The R-squared indicator is a statistical measure of the confidence of the trend. When this indicator moves above its critical level, there is statistically a 95% confidence level that the current trend will continue. However, when the R-squared indicator is below its critical level, it is a warning that the current trend is vulnerable to a reversal in trend. Note that the R-squared indicator remains below its critical level and is a warning that the newly established upward price rally could turn back down. In defense of the R-squared indicator, note that it is still rising. As long as it keeps rising, it will eventually move above its critical level and signal a 95% confidence level that the upward rally will continue.

The third panel from the top of Figure 1 is that of the relative standard error index (RSEI). This, an invention of my own, is derived from the standard error calculation of the linear regression line. The normal standard error indicator is difficult to interpret as the levels vary from security to security. As a result, I have created the RSEI to remove this variation. The standard error and the RSEI are a statistical measure of volatility. The RSEI moves between zero and 1. When the RSEI is below 0.2, it indicates extremely low volatility and when it is above 0.8, it indicates extremely high volatility. Statistically, extreme low volatility normally occurs during a strong rally and extreme high volatility occurs around trend reversals. Note that the RSEI is above 0.8, indicating extreme volatility and warns of a reversal in the intermediate-term trend from down to up.

In conclusion, it appears from this analysis that the DJIA is pulling itself up out of the latest secondary reaction. The volatility of price has become extreme, price has moved above the three signal channel line, and the slope of the linear regression trendline is now sloping upward. All we are waiting for is the R-squared indicator to move above its critical level. Confirmation that price is in an established intermediate-term upward rally would come when the RSEI moves back below 0.2, signaling extremely low volatility and indicating that a strong upward rally is in progress. For now, all eyes are on the R-squared indicator to clarify that the secondary reaction is over and the bull market has resumed.



Alan R. Northam

Alan Northam lives in the Dallas, Texas area and as an electronic engineer gave him an analytical mind from which he has developed a thorough knowledge of stock market technical analysis. His abilities to analyze the future direction of the stock market has allowed him to successfully trade of his own portfolio over the last 30 years. Mr. Northam is now retired and trading the stock market full time. You can reach him at inquiry@tradersclassroom.com or by visiting his website at http://www.tradersclassroom.com. You can also follow him on Twitter @TradersClassrm.

Garland, Tx
Website: www.tradersclassroom.com
E-mail address: inquiry@tradersclassroom.com

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Date: 07/26/11Rank: 2Comment: 
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