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I was wondering what difference and relation are between forecast and prediction? Especially in time series and regression?

For example, am I correct that:

  • In time series, forecasting seems to mean to estimate a future values given past values of a time series.

  • In regression, prediction seems to mean to estimate a value whether it is future, current or past wrt the given data.

Thanks and regards!

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    $\begingroup$ I would be surprised if these terms are well defined so that there is universal answer to this question. $\endgroup$ – JohnRos Jul 23 '13 at 21:04
  • $\begingroup$ What is the difference between prediction, forecast and projection? What is the opperationality of this concepts. $\endgroup$ – user67874 Jan 31 '15 at 14:46
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    $\begingroup$ The IPCC distinguish between a prediction and a projection in the sense that when you make a prediction you mean that unconditionally something will happen (with some probability), whereas a projection is contingent on a scenario, i.e. if we follow this course of action then X will happen (with some probability). If that course of action is not taken, then we shouldn't necessarily expect to see X (at least with the same probability). This distinction makes good sense to me in situations where the future outcome is dependent on events that happen between now and then. $\endgroup$ – Dikran Marsupial Jan 31 '15 at 15:00
  • $\begingroup$ It is hard to generalize single distinction to all domains, but in regression, we can extrapolate already built regression model to new subjects not being in the training sample and predict the outcome (dependent variable). However, in forecasting, we usually look at subject's historical data to build model and then predict certain outcome in future based on the same model. For instance, based on last 10 days electricity usage, we can forecast usage for the same person in 11-12 day, but not for new people. So, already available forecasting model is unlikely to be used for new subjects. $\endgroup$ – Espanta Oct 31 '15 at 4:25
  • $\begingroup$ another difference is that, in prediction, we do not have usually time element. But in forecast we only think about future. Suppose, you want the price of your car today. Using historical data of sold cars in your area, you devise a model and then feed the model with your car detail to get the estimate. However, there is no time element here; you can use the same model to forecast the price of your car, if you can forecast the condition of your car next year (mileage, accident, age (increasing 1 year)). $\endgroup$ – Espanta Oct 31 '15 at 4:34
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Your distinction sounds reasonable. There was a similar discussion at the analyticbridge website, where several people make various distinctions but none of them seem to agree.

The closest one was, "Forecasting would be a subset of prediction. Any time you predict into the future it is a forecast. All forecasts are predictions, but not all predictions are forecasts, as when you would use regression to explain the relationship between two variables."

So as you say, "forecast" implies time series and future, while "prediction" does not.

Note that there is also a term "projection" which is distinct from forecast or prediction, in some disciplines.

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  • $\begingroup$ Thanks! Can you explain the difference between projection and the other two? $\endgroup$ – Tim Jul 23 '13 at 18:02
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    $\begingroup$ @Tim: I'm not totally certain, but in climate circles they talk about projections. I'd like to say that projections are conditional forecasts (conditioned on a specific scenario), but it's evidently more complex than that. A regular forecast is always conditional on "other things remaining the same", of course. $\endgroup$ – Wayne Jul 23 '13 at 18:32
  • $\begingroup$ In demographics I've heard "projection" used to mean a forecast based in current trends. In this sense projection are just a subset of all forecasts, because demographers also do forecasts using educated guesses about how current trends are likely to change. $\endgroup$ – Pere Dec 9 '16 at 0:11
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There is only one difference between these two in time series. Forecasting pertains to out of sample observations, whereas prediction pertains to in sample observations. Predicted values (and by that I mean OLS predicted values) are calculated for observations in the sample used to estimate the regression. However, forecast is made for the some dates beyond the data used to estimate the regression, so the data on the actual value of the forecasted variable are not in the sample used to estimate the regression.

Residuals: Difference between the actual value of Y and its predicted value for observations in the sample.

Forecast error: Difference between future value of Y, which is not contained in the estimation sample, and the forecast of the future value.

Note : This was extracted from Introduction to Econometrics by Stock and Watson (p. 527)

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    $\begingroup$ Thanks! What do you mean by in sample and out of sample? $\endgroup$ – Tim Jul 23 '13 at 21:01
  • $\begingroup$ updated now in the answer $\endgroup$ – Metrics Jul 23 '13 at 21:29
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There is also an etymological difference noted by Nate Silver in The Signal and the Noise:

(...) an ancient idea of prediction—associating it with fatalism, fortune-telling, and superstition—it also introduced a more modern and altogether more radical idea: that we might interpret these signs so as to gain an advantage from them. (...)

The term forecast came from English’s Germanic roots, unlike predict, which is from Latin. Forecasting reflected the new Protestant worldliness rather than the otherworldliness of the Holy Roman Empire. Making a forecast typically implied planning under conditions of uncertainty. It suggested having prudence, wisdom, and industriousness, more like the way we now use the word foresight.

and - as Nate Silver notes - they do have a different meanings in certain fields:

(...) The terms “prediction” and “forecast” are employed differently in different fields; in some cases, they are interchangeable, but other disciplines differentiate them. No field is more sensitive to the distinction than seismology. If you’re speaking with a seismologist:

  1. A prediction is a definitive and specific statement about when and where an earthquake will strike: a major earthquake will hit Kyoto, Japan, on June 28.
  2. Whereas a forecast is a probabilistic statement, usually over a longer time scale: there is a 60 percent chance of an earthquake in Southern California over the next thirty years.

The USGS’s official position is that earthquakes cannot be predicted. They can, however, be forecasted.

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  • $\begingroup$ Liked this answer better. $\endgroup$ – Hamdi Apr 18 '16 at 2:08
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[This was meant as a comment to Tim's answer, which I liked, but it's too long.]

There's a comment by Rasch along the lines of Tim's answer:

First a terminological remark. The "prediction" is suggestive of the statistician as a magician who can tell the future. Economists have an expression that is less pretentious: forecasting – not much more reliable than weather forecasting.

To speak seriously: you do not really predict anything. What you do, is to calculate the distribution of the variate in question, possibly offering its mean value or the like as a likely event – but only on the assumption that the model – or a characteristic feature of it – on which you based this forecasting, still holds, i.e. confronted with what eventually does happen you are faced with a test of this hypothesis and nothing else – you were not telling what the future would be!

on p. 268 of "Sufficiency, prediction and extreme models" by Lauritzen (Barndorff-Nielsen & al, eds: Conference on foundational questions in statistical inference, Aarhus 1973).

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