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All have the same trend, but more filtering leads to higher r 2 of fitted trend line. The least-squares fitting process produces a value, r-squared (r 2), which is 1 minus the ratio of the variance of the residuals to the variance of the dependent variable. It says what fraction of the variance of the data is explained by the fitted trend line.
In finance, a trend line is a bounding line for the price movement of a security. It is formed when a diagonal line can be drawn between a minimum of three or more price pivot points. A line can be drawn between any two points, but it does not qualify as a trend line until tested. Hence the need for the third point, the test.
Trend line can refer to: A linear regression in statistics; The result of trend estimation in statistics; Trend line (technical analysis), a tool in technical analysis
A trend line could simply be drawn by eye through a set of data points, but more properly their position and slope is calculated using statistical techniques like linear regression. Trend lines typically are straight lines, although some variations use higher degree polynomials depending on the degree of curvature desired in the line.
Since either a reversal or a trading range follow a valid trendline violation, it's evident that upside momentum has temporarily dissipated, causing the KST to cross below its moving average. Traditionally, the MACD gives buy and sell signals when it crosses above and below its exponential moving average, known as the “signal line”.
The above matrix equations explain the behavior of polynomial regression well. However, to physically implement polynomial regression for a set of xy point pairs, more detail is useful. The below matrix equations for polynomial coefficients are expanded from regression theory without derivation and easily implemented. [6] [7] [8]
A more common version of line break charts is a “three-line break” chart, which indicates that for a market reversal to occur (a new line that forms in the opposite direction to the previous lines), the price will have to break above or below the previous three lines depending on the direction of the lines. [9]
Trends do not have to be linear or log-linear. For example, a variable could have a quadratic trend: = + + +. This can be regressed linearly in the coefficients using t and t 2 as regressors; again, if the residuals are shown to be stationary then they are the detrended values of .
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