|In the world of statistics, data is collected through various methods including but not limited to experiments, surveys, and polls. This data is then analyzed using statistical methods of analysis to determine things such as the trend in the data, how strong the trend is, and its error. |
Each day, Gallup performs a telephone interview of 1,500 adults to determine if Americans think the economy is getting better or getting worse. The recently published results of this survey show that 76% of Americans think that the economy is getting worse and 19% think it is getting better. Gallup also published that there is a +/-3% error in the results of the survey.
In looking at a graph of the data, it can be seen that Americans think the economy is worsening (http://www.gallup.com/poll/110824/Gallup-Daily-US-Economic-Outlook.aspx).
|The same methods of analysis that Gallup uses in analyzing the data they collect can be applied to any set of collected data, including the daily price change of an individual security or an entire market. |
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) drawn through 200 days of daily closing price of the DJIA and then extended forward in time. The 200-day linear regression upper and lower two sigma channel lines are also shown, as are the upper and lower three sigma channel lines (green dotted lines).
The linear regression line itself (the middle green line) represents the primary trend of the market 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 that 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. 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 change in trend is virtually assured.
|In Figure 1 it can be seen that price has now moved outside the upper and lower two sigma channel lines. Movement outside the upper or lower two sigma lines does occur once in a while and then moves back inside the channel lines. When a single data point moves outside the channel, it is called an outlier and is usually excluded from the data. However, when more than one data point moves outside the two sigma channel line, it can be a warning that a change in trend is in progress. Figure 1 shows that the closing price of the DJIA has now been below the lower two sigma channel line for three consecutive days now and sends a strong warning that a change in trend is in progress.|
|FIGURE 1: .DJI, DAILY. This chart shows the daily price chart of the DJIA, along with the 200-day linear regression trendline and its upper and lower two and three sigma channel lines.|
|Graphic provided by: MetaStock.|
|Figure 1 also shows that price has not yet moved below the lower three sigma linear regression channel line. A move outside the three sigma channel line is a rare event and generally signals a change in trend. As such, if the long-term uptrend in the DJIA is to continue, then the lower three sigma channel line should represent a strong line of support to the primary bull market trend. However, if the primary bull market trend is over and a new primary bear market trend is emerging, then the lower three sigma channel line should be successfully violated by a series of two or more successive closing prices falling below this channel line.|
|In conclusion, the long-term statistical analysis of the DJIA shows that price has now fallen below the lower two sigma linear regression channel line and has remained below this line for three consecutive days. As a result, we cannot discount the closing prices as outliers and remove them from the data but must consider that these three closing prices represent that a change in the trend of the data as taking place from a long-term uptrend known as a primary bull market to a long-term downtrend known as a primary bear market. A successful breakdown below the lower three sigma channel line will help confirm this change in trend.|
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