|Figure 1 shows the daily bar chart of the Dow Jones Industrial Average (DJIA) from October 2011 onward. The vertical blue line is drawn on the chart from the most recent highest peak of the linear regression slope indicator. This peak represents the maximum point of price acceleration. |
The linear regression trendline (blue line) is drawn from this point back in time over the preceding 50 trading sessions representing the intermediate-term trend. The linear regression trendline is then extended to the right of the vertical blue line. The vertical blue line was originally drawn in early February, representing the future price trend.
The plus and minus one sigma channel lines, the plus and minus two sigma channel lines, and the plus and minus three sigma channel lines are also drawn in like manner. The 50-session linear regression slope indicator is shown in the top panel and the R-squared indicator in the middle panel.
|FIGURE 1: .DJI, DAILY. This chart shows the daily price chart of the DJIA in the bottom panel along with its 50-day linear regression line. The linear regression slope indicator is shown in the top panel, and the R-squared indicator is shown in the middle.|
|Graphic provided by: MetaStock.|
|The linear regression slope indicator shows when the intermediate-term trend begins and ends as well as how fast price is accelerating or decelerating. Note that this indicator crossed above its zero line in October 2011, indicating a reversal in trend from down to up. |
From October onward, this indicator shows two periods of price acceleration when it was moving in an upward direction. This indicator also shows two periods of price deceleration when it moved in a downward direction, with the second period ending May 11 when the linear regression slope indicator moved below its zero line. Once this indicator moved below its zero line, it began to indicate a reversal in trend from an uptrend to down. Note that the most recent intermediate-term uptrend lasted seven months from when the linear regression slope indicator moved above its zero line until it moved below its zero line.
|The R-squared indicator in the third window is a measure of the strength of the trend. The scale of the R-squared indicator moves from zero (0.0%) to 1 (100%). When this indicator is at zero, it indicates that all price movement is random and there is no trend. When this indicator is at one, it indicates that all or 100% of price movement is trending. When this indicator is at 0.5, it indicates that 50% of the price movement represents the trend and 50% of the price movement is random. |
Currently, this indicator is reading 0.3, indicating that 30% of the price movement is trending and the other 70% of the price movement is random. This is normal at the beginning of a newly established trend. Note that the direction in which the R-squared indicator is moving suggests that the current trend is strengthening and should continue to strengthen as the new trend continues to advance.
There is another statistical measurement of the R-squared indicator in the form of its critical level. The critical level is represented by a horizontal line that moves up or down based upon the lookback period. For a 50-session lookback period, this line is drawn at 0.08. When the R-squared indicator is above this line, it indicates the existence of a statistical significant trend with a 95% confidence level that the trend will continue. When the R-squared indicator is below the critical level, that statistical significance no longer exists. Note that the R-squared indicator is currently above this critical level, indicating a statistically significant downtrend.
|Looking at the price chart in the bottom panel shows that from early February 2012 onward, price started to fall away from the linear regression trend line (upsloping blue line). This falling away is known at price deceleration. Price deceleration normally is a sign of a weakening trend and a sign that the uptrend has just about run its course and a reversal in trend is on the horizon. |
Note that in mid-April price moved below its -2 sigma channel line, sending a warning that a reversal in trend is ahead. An actual reversal signal is given when price moves below the -3 sigma channel line. Note that in April there were two false signals of a trend reversal. False signals do not happen often but do occur from time to time.
I normally like to set a filter to minimize false signals. The filter I normally use is to wait for a second consecutive lower close to signal a reversal. On May 4, a third reversal signal was given and on May 7, the next trading session, a second consecutive lower close gave the official signal that an intermediate-term reversal from up to down had occurred. Note that since the official reversal signal, price has continued to move lower.
|This statistical analysis shows that on May 4, the DJIA moved below the -3 sigma channel line and on May 7, price made a second lower close below the -3 sigma channel line to signal a reversal in trend from up to down. On May 11, the linear regression slope indicator moved below its zero line to signal a reversal in trend from up to down. (Sometimes the linear regression slope indicator moves below its zero line before price moves below the -3 sigma channel line.) On May 16, the R-squared indicator moved back above its critical level to indicate that the newly established intermediate-term downtrend had become statistically significant, meaning that there is now statistically a 95% confidence level that the downtrend will continue. |
To complete a reversal in trend from up to down, price must move below its -3 sigma channel line, the linear regression slope indicator must move below its zero line, and the R-squared indicator must move above its critical level.
Once a new trend has been established, the linear regression trendline and its associated channel lines can be redrawn to show the new trend (not shown on the chart). Now that the intermediate-term trend has reversed, we should expect to see the DJIA continue to move lower over the months ahead.
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