[- forecasting methods]
b-2) EXTRAPOLATION METHODSwikipedia.com - "in mathematics, extrapolation is the process of constructing new data points outside a discrete set of known data points"
although there are no essential differences between extrapolation & interpolation methods, the expected accuracy from their results do differ quite appreciably; this fact and the main intention underlying the present clasiffication [highlighting the opposition probable/predictable vs. random/unpredictable] are the only reasons explaining this specific subtype (outside the regression methods)
nobody doubts that an increase in the uncertainty is the immediate consequence of any extrapolating process, however the logical attitude resulting from this idea [no extrapolating] seems to be not so clear; or, at least, this is what anyone could understand after noticing the wide variety of existing extrapolation methods
- linear extrapolation
- polynomial extrapolation
- conic extrapolation
- french curve extrapolation
and, even, methods specifically developed for computer coding
- Richardson extrapolation
- Aitken extrapolation
extrapolating has to be considered as the last resource and, in any case, to be clearly differentiated from interpolating
a lame example
raw data - X (independent) ∈ [5,10] and Y(dependent) ∈ [10,20]
* Y values, for any X within the aforementioned range, may be predicted - 7.5 -> 15
* on the other hand, Y values, for X outside it, may only be rougly estimated - 15 -> 30
thus, predicting implies uncertainty but, usually, a more or less controllable one [a sensible set of minimum conditions has to be stablished in order to guarantee the predictive character] - (roughly) estimating implies uncontrollable uncertainty, hence should be used just as a preliminary idea and its results never be called "predictions"
nobody doubts that an increase in the uncertainty is the immediate consequence of any extrapolating process, however the logical attitude resulting from this idea [no extrapolating] seems to be not so clear; or, at least, this is what anyone could understand after noticing the wide variety of existing extrapolation methods
- linear extrapolation
- polynomial extrapolation
- conic extrapolation
- french curve extrapolation
and, even, methods specifically developed for computer coding
- Richardson extrapolation
- Aitken extrapolation
trendingBot point of view
a lame example
raw data - X (independent) ∈ [5,10] and Y(dependent) ∈ [10,20]
* Y values, for any X within the aforementioned range, may be predicted - 7.5 -> 15
* on the other hand, Y values, for X outside it, may only be rougly estimated - 15 -> 30
thus, predicting implies uncertainty but, usually, a more or less controllable one [a sensible set of minimum conditions has to be stablished in order to guarantee the predictive character] - (roughly) estimating implies uncontrollable uncertainty, hence should be used just as a preliminary idea and its results never be called "predictions"
