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STATISTICS


Primary Bull Market Remains Intact

07/21/11 11:23:25 AM
by Alan R. Northam

Statistical analysis is used to show that the primary bull market of the Dow Jones Industrial Average remains intact. However, this analysis also shows that a market top lies ahead.

Security:   .DJI
Position:   N/A

Any analysis, whether technical or statistical, of any stock or market must begin with the long term as it is here that the analyst or trader finds the primary trend. One of the basic tenets of trading states that high-probability trades are found in the direction of the primary trend.

Charles Henry Dow once stated that a primary trend is a trend that lasts for more than a year. While there is approximately 250 days in a trading year, it has generally become common practice to use a 200-day lookback period in defining the primary trend.

The bottom panel of Figure 1 shows the daily price bars of the Dow Jones Industrial Average (DJIA). This panel shows the 200-day linear regression line (middle upsloping blue line) along with its upper and lower two sigma channel lines. The linear regression line (the middle line) represents the primary trend and is often referred to as the linear regression trendline. The upper and lower two sigma channel lines represent the range in which price statistically moves 95% of the time.

In the majority of cases, once price moves outside the two sigma channel lines, a signal is given that there is a high probability a change in the direction of the trend lays ahead. However, 5% of the time price may move outside the two sigma channel lines before moving back inside the two sigma channel lines. Note that in Figure 1 price continues to move inside the upper and lower two sigma channel lines. As long as price remains within these boundaries, statistically, the DJIA is said to be in a primary bull market.

FIGURE 1: DJIA, DAILY. This chart shows the daily price chart of the Dow Jones Industrial Average, in the bottom panel along with the 200-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 primary trend. The last time this indicator moved above its zero line to signal the beginning of a new primary trend was in October 2010. When this indicator moves upward, it indicates price acceleration. When this indicator is moving sideways, it indicates that price is neither accelerating nor decelerating but is increasing at a constant rate compared to the price from 200 days ago. When this indicator is moving down while still above its zero line, it indicates price deceleration, which normally starts to occur near the end of a trend.

As can be seen in the top panel of Figure 1, the linear regression slope indicator is moving down, indicating that price is in its deceleration stage and is signaling that the end of the primary trend is approaching. Please note, however, that while price is in a deceleration stage, it can still make a new high before the trend is complete.


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. The last time the R-squared indicator moved above its critical level to signal that there was a 95% confidence level that the primary trend would continue was at the end of October 2010 shortly after the linear regression slope indicator moved above its zero line to signal that a new primary trend had developed. Note that since that time the primary trend has moved higher.

Note that the critical level varies with the length of the lookback period. For example, a 200-day lookback period has a critical level of 0.03 and a 20-day lookback period has a critical level of 0.2. To determine these critical levels, a complicated mathematical process within statistics is used, and thus, tables are normally used.

When the R-squared indicator falls back below its critical level, there is no longer a high level of confidence in the trend and the trend becomes vulnerable to a change. Note that the R-squared indicator has now started to fall. Normally, once this process starts, it doesn't stop until the R-squared indicator crosses below its critical level. However, on occasion the R-squared indicator does turn back up and the trend continues. In addition, please note that while the R-squared indicator is falling, it is still possible for the price to make a new higher high before the R-squared indicator crosses below its critical level.

The third panel from the top of Figure 1 is that of the relative standard error index (RSEI). This 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 0.2, indicating that volatility has started to increase, suggesting that price is now starting to enter an area in which a reversal in direction could lay ahead. However, a better indication would be when the RSEI moves above 0.5.

In conclusion, the primary bull market of the DJIA remains intact. However, statistical analysis suggests that a reversal in trend is ahead.



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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