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 with respect to the given data.
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.
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:
- 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.
- 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.
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)
[This was meant as a comment to Tim's answer, which I liked; but it's too long to be posted as a comment.]
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).
Personally I prefer to use "prediction" when a hypothesis assigns probability 1 (or 0) to some statement, and to use "forecast" otherwise. Because that hypothesis is then acting as a sort of physical theory with regard to that statement.
But also in that case the "prediction" is not guaranteed to be correct. Unit probabilities always come about from some simplification (which may be necessary for computational purposes) in our assumptions and beliefs.
