1992issue C031-3
Constructing log-linear growth-rate baselines
A growth-rate baseline is built by fitting a least-squares line to ordered observations after a natural-log transform, converting the slope back to a period percentage, and reading the coefficient of determination as a check on that path.
- A growth-rate baseline is constructed by fitting a least-squares line to ordered observations, with the intercept taken at a time index of zero and the slope read as the rate of change.
- A natural-log transform places the series on a percentage-change scale so the fitted slope estimates a growth rate rather than a raw increment.
- The log-space slope is converted back by exponentiating, subtracting one, and multiplying by one hundred to express the period growth rate.
- The coefficient of determination indexes how closely percentage growth follows an exponential path and is read before any later forecast is compared with the baseline.
Fitting an explicit baseline
A growth-rate baseline can be constructed by fitting a least-squares line of the form Y = a + bX to ordered observations. The intercept a is the fitted value of the series when the time index equals zero. The slope b is the fitted rate of change.
A least-squares line is a straight line fitted so the total squared vertical error between the line and the ordered observations is minimized. Overlaying that fitted line on the plotted series is the visual counterpart of the constructed baseline.
Reading the slope as a growth rate
Converting the series to natural logarithms replaces each observation with its natural logarithm so later changes are measured on a percentage scale. The fitted slope then estimates a growth rate rather than a raw increment.
After estimation in log space, the slope is converted back by exponentiating, subtracting one, and multiplying by one hundred. That conversion expresses the period growth rate.
Partial-year time indexes
When the latest earnings observation covers only the first quarter, the matching time index is set to a fractional value such as 4.25 instead of a full extra year. Two quarters use 4.50. A fractional time index is a non-integer time coordinate used when the latest observation covers only part of a sampling year.
A check on the exponential path
The coefficient of determination is obtained by squaring the correlation coefficient. It indexes how closely percentage growth follows an exponential path, with 100 as a perfect fit and 0 as none.
The same construction for earnings
The same log-linear construction used for dividends applies to earnings by substituting natural logarithms of fiscal-year earnings as the dependent variable.
All readings on this track · 43 readings
- 1990Constructing dollar baselines from rates, inflation, and residuals
- 1990Constructing a nominal index value from forward earnings and fitted yield
- 1990Constructing a nominal index price from earnings and a fitted yield
- 1990Endpoint-pinned price paths are not forecasts
- 1990Constructing least-squares polynomial smoothers
- 1991Endpoint growth rates versus linear-regression consistency
- 1991Out-of-sample checks for linear growth fits
- 1991Trend as persistence, not a straight line
- 1991Quadratic trend, residual oscillator, and a secondary cycle calendar
- 1991Time-origin offset and residual-price divergence on a quadratic least-squares fit
- 1991A least-squares trendline from ordered prices
- 1992Constructing log-linear growth and reliability screens
- 1992Constructing log-linear growth-rate baselines
- 1992Next-session high, low, and close from rolling linear regression
- 1993Auditing an index price-earnings multiple with short-rate regression
- 1994Regression-seeded nested exponential price filter
- 1994Constructing the double exponential average from lag cancellation
- 1994Evaluating money supply as a linear leading-index baseline
- 1995Constructing least-squares trend channels
- 1995Linear baseline holdout checks for annual bill-rate forecasts
- 1995Projection bands from high and low regression slopes
- 1995Evaluating a least-squares end-point moving average on a known test series
- 1996Constructing an endpoint moving average from a least-squares line
- 1996Scoring equity path consistency with a k-ratio overlay
- 1996Evaluating month-end yield gaps for equity regimes
- 1996Constructing session-indexed standard error bands
- 1998Evaluating linear regression baselines for index valuation
- 1998R-squared as a two-state trend filter from a price-time fit
- 2000Second-order moving-average lag correction
- 2002Price regression line versus beta for index tracking
- 2003Regression slope with an r-squared trend confidence gate
- 2003Constructing finite-volume-element divergence with slope comparison
- 2004Building a daily score from regression, retracement, and volume
- 2004Constructing least-squares trendlines from ordered prices
- 2007Rectangle breakout targets beyond height
- 2007Confirming a price trend with regression slope and r-squared
- 2008A linear-regression angle assembled as one trend filter
- 2010A two-state swing machine from four running extremes
- 2016Score oil-complex tightness before divergence or regression
- 2017Nikkei-yen intermarket divergence as a regime case study
- 2017Constructing Calmar ratio and linear regression baselines
- 2019Pair-trade layer construction versus average-spread management
- 2020A convolution slope built from nested linear regression