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I was reading about forecasting at Wikipedia: Forecasting and I noticed that in the publication they separate the Naïve, Average and Drift approach from the Time series methods (which involve AR, MA, ARMA, ARIMA, exponential smoothing models...). This is a little confusing for me, because I understood that all of these methods were Time series methods. What is the difference between these forecasting approaches and the "Time series methods"?.

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The distinction made in the Wikipedia article isn't particularly meaningful, especially given that some of the methods that appear in their own sections also appear under "Time series methods" (e.g. what they called "average approach" and the page for "moving average" are the same thing).

One useful distinction, and what the article may have been trying to get at, is the one between methods which:

  1. Provide only a forecast function, that is, a mapping from the data to a point forecast. The "naive" method falls under this category.

  2. Define a complete probabilistic model for the dynamics, typically in the form of the transition law $p(Y_t|Y_1, ..., Y_{t-1})$. In that case, a forecast function can be derived from this probabilistic model, usually as the solution to an optimization problem (e.g. the conditional expectation is optimal in a least squares sense). Models in this category allow for a natural quantification of forecast uncertainty in the form of prediction intervals. ARIMA models fall in this category.

So, while there is indeed an ARIMA model which produces the exact same point forecasts as the average, naive or drift method, conceptually they are entirely different approaches.

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  • $\begingroup$ Ok! that is the difference between methods. Today in class I understood that each method provides a forecast function (I thought that forecast functions where something apart from the methods). Your answer serves me to strenghten that idea. Just to clarify, each and every single one of these methods are "Time series methods" right? and also: which are the methods that provide a probabilistic model like you said? $\endgroup$ – fran496 Feb 14 at 14:02
  • $\begingroup$ @fran496 Your instructor may have a different opinion but there's not really any meaningful reason to argue against calling any method of producing forecasts a "time series method". The classical probabilistic models are things like ARIMA, VAR, general state space models, etc. Exponential smoothing methods are in a weird spot where historically they started as simple forecasting functions but more recently were recognized as corresponding to certain types of state space models, so depending on who you talk to they may consider them to have a full predictive distribution or not. $\endgroup$ – Chris Haug Feb 15 at 14:23

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