matrix:forecast-compound-growth

matrix:forecast-compound-growth data-list

Reports a four-element list of the form:

[ forecast constant growth-proportion R² ]

Whereas matrix:forecast-linear-growth assumes growth by a constant absolute amount each period, matrix:forecast-compound-growth assumes that Y grows by a constant proportion each period. The constant and growth-proportion are the parameters of the trend-line

Y = constant * growth-proportion^t.

Note that the growth proportion is typically interpreted as growth-proportion = (1.0 + growth-rate). Therefore, if matrix:forecast-compound-growth returns a growth-proportion of 1.10, that implies that Y grows by (1.10 - 1.0) = 10% each period. Note that if growth is negative, matrix:forecast-compound-growth will return a growth-proportion of less than one. E.g., a growth-proportion of 0.90 implies a growth rate of -10%.

NOTE: The compound 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-compound-growth will result in an error if it finds a zero or negative number in data-list.

;; a compound growth extrapolation of the next item in the list.
print matrix:forecast-compound-growth [20 25 28 32 35 39]
=> [45.60964465307147 21.15254147944863 1.136621034423892 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 * 1.1366 ^ t
;; * Y grows by approximately 13.66% each period
;; * the R^2 value is roughly 0.9761 (a good fit)