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I believe it fits under the definition from wiki:

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

Am I right?

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No. An interpolation is a function that pass exactly through the observed data points. For example, a polynomial with sufficient degree (the number of points less one), or a Fourier trigonometric expansion (if the function is assumed periodic).

The forecasting methods are approximations. They do not pass exactly by the observed points, but near by. Which allows for the function to be smoother.

Furthermore, the Holt-Winter method is discrete. It does not give a approximate value for time in between observed data points, but gives point for the next time values. So the word would be extrapolation (extra=out-of) rather than intrapolation (intra=inside). But, it is not an extrapolation because it an approximation rather than exact values.

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