1988issue C081-5
Treat a suspected bend as a construction test
A curved trendline can describe a flattening or accelerating path more usefully than a straight trendline. Apparent upward curvature can be arithmetic-scale-distortion, and a second-degree-parabola is presented as a follow-up when a curved path is expected to fit better than a linear-regression.
- When a plotted series flattens with a downward bend or accelerates upward, a curved trendline can describe the path more usefully than a straight trendline.
- Apparent upward curvature can be arithmetic-scale-distortion, and logarithmic-rescaling can restore a linear description.
- A second-degree-parabola is a least-squares follow-up to linear-regression, with a quadratic-coefficient that is positive when the curve turns up and negative when it levels off.
- Editorial reading: add that signed deviation only when the residual still has a directional shape that later price can disprove.
When a curve describes the path better
When a plotted series flattens with a downward bend or accelerates upward, a curved trendline can describe the path more usefully than a straight trendline. A trendline is a constructed path through plotted observations, kept straight or allowed to bend, so a later break can confirm or reject the hypothesized trajectory.
Check the scale before accepting the bend
Apparent upward curvature can be an artifact of arithmetic-scale-distortion, because a given percentage rise looks larger near the top of the plot than near the bottom. Chart-scale-analysis is a check of whether arithmetic or logarithmic scaling is creating, hiding, or exaggerating apparent curvature in the same price path.
Logarithmic-rescaling replaces raw levels with their logarithms, or plots the series on a logarithmic scale, so a straight trendline can be fitted after that percent-move distortion is removed. A logarithmic scale, or a straight-line fit applied to the logarithms of the observations, can restore a linear description.
How the curved path is located
A curved trendline can be constructed by freehand drawing, by approximate template fitting, or by a least-squares-fit. Linear-regression is the least-squares straight-line baseline fitted to ordered observations and used as the first quantitative description before any curvature term is added.
A standard mathematical construction is a second-degree-parabola. It keeps the straight-line intercept and slope and adds a quadratic term to measure how far the path bends away from that line. The quadratic-coefficient is the signed constant on the squared term: positive when the fitted curve turns upward and negative when the fitted curve levels off.
Add the parabola only after the linear baseline
The quadratic construction is presented as a follow-up when a curved path is expected to fit the observations better than a linear-regression. Locating that curve requires estimating three constants, and the historical workflow carries out the construction with a seven-column spreadsheet procedure, a worked numerical example, and a plotted result.
A higher coefficient of determination for an exponential curve than for a linear fit may be read as a sign of slowing momentum or a change in trend.
All readings on this track · 14 readings
- 1982Constructing semi-log scales for trend channels
- 1988Treat a suspected bend as a construction test
- 1989Constructing percentage-box point-and-figure charts
- 1989Constructing point-and-figure objectives across chart scales
- 1991Unfinished point-and-figure until filter, scale, and pivots measure percent
- 1992A logarithmic point-and-figure construction with weekly breadth scores
- 1995Constructing a least-squares trend channel with two-standard-deviation rails
- 1995Percentage boxes turn a three-box reversal into a scale decision
- 2003Log scale trendlines and compound growth
- 2007Trendline and channel construction on linear versus log scales
- 2012Constructing trend-intensity overlays across chart scales
- 2015Index drawdown caps, chart-scale stops, and leverage
- 2016Evaluating breakouts by share-price band
- 2016Constructing chart scale with a golden-rectangle aspect ratio