matrix:forecast-continuous-growth

matrix:forecast-continuous-growth data-list

Reports a four-element list of the form:

[ forecast constant  growth-rate  R² ]. Whereas matrix:forecast-compound-growth assumes discrete time with Y growing by a given proportion each finite period of time (e.g., a month or a year), matrix:forecast-continuous-growth assumes that Y is compounded continuously (e.g., each second or fraction of a second). The constant and growth-rate are the parameters of the trend-line

Y = constant * e^{(growth-rate * t)}

matrix:forecast-continuous-growth is the “calculus” analog of matrix:forecast-compound-growth. The two will normally yield similar (but not identical) results, as shown in the example below. growth-rate may, of course, be negative.

NOTE: The continuous growth forecast is achieved by taking the ln of Y. (See matrix:regress, below.) Because it is impossible to take the natural log of zero or a negative number, matrix:forecast-continuous-growth will result in an error if it finds a zero or negative number in data-list.

;; a continuous growth extrapolation of the next item in the list.
print matrix:forecast-continuous-growth [20 25 28 32 35 39]
=> [45.60964465307146 21.15254147944863 0.12805985615332668 0.9760867518334806]
;; These results tell us:
;; * the next predicted value is approximately 45.610
;; * the compound growth trend line is given by Y = 21.1525 * e ^ (0.1281 * t)
;; * Y grows by approximately 12.81% each period if compounding takes place continuously
;; * the R^2 value is roughly 0.9761 (a good fit)