Prediction is the more general statement. A prediction (predicted value) is an expectation for a combination of predictors (predictor values). The prediction is calculated based on a model, and the model is usually obtained by a fit to some available data.

The most simple example is the mean of a sample. The model is most simple - there is no particular predictor involved (you only have some values for some response variable but you do not have any information on what these values may depend). The mean is the model that maximizes the likilihood (of the data under the model). It gives the expected value for the response. This means: if you had to make a guess abut any new value that is obtained in a similar way how the sample was obtained, the sample mean is your best guess.

If you know that the data depends on the membership to a group (e.g. "controls" and "treated"), then you have a (categorical) predictor (the group) and a model using this predictor gives you an expected value for each group (group means). Thus, based on a given group membership you can calculate what value to expect.

The predictor may be continuous as well (like "time"). In this case the model gives you an expected value for any possible value of this predictor. Here it is possible to predict value at time points for which no data exists. When such a prediction is done for times within the range of observed time points it is called an interpolation. When the prediction is done outside of the range of observed time points it is called an extrapolation. So far this all applies to any kind of continuous predictor (like concentration, mass, distance, speed, ...). The "time" is somewhat special because it has a natural "direction" (from past to future), and time-series analyses are usually performed to make predictions of future observations - this is called a forecast.

Prediction is the more general statement. A prediction (predicted value) is an expectation for a combination of predictors (predictor values). The prediction is calculated based on a model, and the model is usually obtained by a fit to some available data.

The most simple example is the mean of a sample. The model is most simple - there is no particular predictor involved (you only have some values for some response variable but you do not have any information on what these values may depend). The mean is the model that maximizes the likilihood (of the data under the model). It gives the expected value for the response. This means: if you had to make a guess abut any new value that is obtained in a similar way how the sample was obtained, the sample mean is your best guess.

If you know that the data depends on the membership to a group (e.g. "controls" and "treated"), then you have a (categorical) predictor (the group) and a model using this predictor gives you an expected value for each group (group means). Thus, based on a given group membership you can calculate what value to expect.

The predictor may be continuous as well (like "time"). In this case the model gives you an expected value for any possible value of this predictor. Here it is possible to predict value at time points for which no data exists. When such a prediction is done for times within the range of observed time points it is called an interpolation. When the prediction is done outside of the range of observed time points it is called an extrapolation. So far this all applies to any kind of continuous predictor (like concentration, mass, distance, speed, ...). The "time" is somewhat special because it has a natural "direction" (from past to future), and time-series analyses are usually performed to make predictions of future observations - this is called a forecast.

There is an interesting debate on this topic at the following link

http://stats.stackexchange.com/questions/65287/difference-between-forecast-and-prediction

Predictions are based on arbitrary methods/experiences, mostly seen in astrology, numerology, etc... However forecasts are based on scientific methods,which involve the historical data, example time series.

I do economic forecasts, and because data lags, I have to predict what the close of 2014 will be when generating my 2015 forecast in January.

Thanks Rudy for asking this question. Prognosis is another term which I found is sometimes being used synonymously with forecasting or prediction. Is this technically right?

This is one of  interesting questions to ask future statisticians. I thought carefully of an educated and articulate response to this question. All I could really come up with was, yes, I guess there is  difference between two terms, in terms of Logic. Then I had been looking in literature for so long. The words `prediction' and `forecasting' are used interchangeably throughout most of published articles. Furthermore they are employed differently in different fields. In general, one could make abusive use of the two terms (foracasting vs predictions), but as soon as we want to measure the predictability or forecastability of time series, the subtlety of the two terms becomes necessary.

For a detailed discussion of these different

definitions, see Clements and Hendry (1998, chapter 2) and this article (http://jmlr.org/proceedings/papers/v28/goerg13.pdf).

Briefly, predictability is defined as a property of a random variable in relation to an information set (the conditional and unconditional distributions of the variable do not coincide). It is a necessary, but not sufficient condition for forecastability, as the latter requires knowledge of what information is relevant and how it enters into the causal mechanism.

Along with the great majority of researchers and practitioners, such technical niceties are usually  ignored and the two words will continue to be regarded as synonyms.

http://books.google.fr/books?id=aJ966QLx0WAC&printsec=frontcover&hl=fr&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

http://jmlr.org/proceedings/papers/v28/goerg13.pdf

Article Forecastable Component Analysis (ForeCA)

The major difference is that forecasting can have error, that is why we have confidence interval of 5%, 2.5%, 1% and residuals for modeling. There is no such thing as so called "perfect forecasting", but we can maximize the model accuracy. I recommend reading Paul's work here: http://odajournal.com/. In contrast, prediction sometime can be perfect, not only from forecast but experience, ingenuity, and theories as well, even psychic or magic. I also believe that model should follow data not the other way around.

Can forecasting help predict something? Yes.

Can forecasting produce a perfect prediction? No.

That is why we cannot totally rely on weather forecast, but take it with our past experience and other factors to be better prepared for any possible contingencies.

Steven has pointed out one very important point that forecasting always has lags and delays, which tries to predict the future, but as we all know future can change indefinitely without any certainty. That is where residuals come into play to model such uncertain behavior. The better one can model such behavior, the better or more adaptive the model will become. Therefore, residuals can be dynamic, stochastic or both dynamic and stochastic. Another example is that the current week real weather condition can be drastically different from last week's forecast, like it is supposed to be sunny but instead snowy.

Eliab, Prognosis is a special case of forecasting particular disease or ailment. It is important, but doctors have to rely on other means such as experience and actual symptom to get a good but not perfect diagnosis. 

So far, looking at the replies to this question leads me to almost the same discussions that I read in the internet. Jochem's reply somewhat provides thin demarcation line between definition and application of "prediction" and "forecast". I agree that prediction involves predictor variables while forecasting involves time. But both techniques can handle/involve "time" and "predictor variables", is this correct? I mean, when we do ARIMA analysis, the lags of the variable in the model are similar to that of predictor variables? and prediction models is not only confine to panel data but time series as well of different variables? 

For Juehui, yes, forecast has error or maybe term as confidence interval at certain level of probability of occurrence. But prediction models also has error component, the plus epsilon at the end of the model that serves as the "dumping" bin of unaccounted observations of the model due to randomness of the data.

Thank you to all of you who shared your knowledge about the topic and maybe more can add additional knowledge. This is getting interesting already. Well keep this loop updated every time i get new information from other sources.

Prediction is the usual (common) term used in sciences other than meteorology and economics. Otherwise, the two may be used interchangeably as pointed out by @Ouaret already.. Accordingly,  the term "forecasting" is used when it is a time series and we are predicting the series into the future (e.g., weather forecasts, etc.). On the other hand, "prediction" is the act of predicting in a cross-sectional setting, where the data are a snapshot in time. Here the modeler is interested to use the information on a sample of records to predict the value of other records (often in future or some kind of extrapolation).

Rudy -

I think of prediction as estimating from regression for missing data in a current time frame, involving continuous data. That is my experience, and that of many economists and survey statisticians, according to much literature. But I'm not saying others may not have a different perspective, and different applications.

In sampling from finite populations, we need to estimate for missing data, or we could just be imputing for nonresponse in a census. Either way, we predict based on a set of y data from a population as related in regression to x data. The x data are for the entire population, and the predicted y values fill in for missing y data. We can estimate the variance of the prediction error (see Maddala, for example), the square root of which is SDSI in SAS PROC REG, and likely found in other software.

On the other hand, forecasting involves time series data, generally for individual respondents.

So to me, a prediction is based on one data set related to another data set or data sets, as a whole, or better, in strata, whereas a forecast follows an individual respondent.

This is why I have noted that for missing establishment survey data, prediction is generally better than forecasting. If we predict based on sets of respondents, then an economic trend could be broken, but this kind of regression will capture this. If, for example, the y values are from a current sample, and we have one regressor, x, which is the same item/variable from a census, this is not really a forecast, but a kind of 'growth' rate between just two periods. Another example of prediction would have current census data for a related variable (say y is a sample of electric generation, and x is from a census of plant capacity, all at the same time period). At any rate, the prediction is all about what is happening 'right now' (or close).

However, if we forecast for individual missing respondents, then if there is a break in the time series, now, a forecast cannot catch that. It does not use the group data. (I think this is probably why Terry Moore, in a question I submitted about small area estimation, said that, in a sense, we are always 'borrowing strength.' That is my take anyway.)

So I'd say that prediction involves data groups, whereas forecasting looks at longer time series for individual respondents. A time series might sometimes do better for an individual imputation, but if your goal is to know a general situation that is rather current, and you can use prediction instead of forecasting, as defined here, the prediction should be a better option. Often your goal is to know when a time series is broken. A forecast based on a time series cannot do that.

Cheers - Jim 

PS - An estimated variance of the prediction error can be done for estimated totals. See the first few pages of the first paper linked here, and the second if you want to know more about this. 

Article Using Prediction-Oriented Software for Survey Estimation

Conference Paper Projected Variance for the Model-based Classical Ratio Estim...

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.

Prediction sounds more like predictive modeling and statistical theory. Forecast sounds like something anyone can do (does not require analytics background), or something based on time series analysis (econometrics), or weather forecasts.

Juehui, thanks for your answer. By the way, do you imply that prognosis is specifically a medical term? I believe, prognosis (as a special case of forecasting) if based on data-driven techniques such as machine learning and pattern recognition, may also be used as well in several industrial applications, e.g., in manufacturing, say, to monitor the health of equipment, etc.

Hi Rudy,

I am not talking about prediction models. In fact, all model has error component as I stated, which controls the model behavior. I am discussing the definition of prediction philosophically. But thanks for bringing up such model.

I am also not recommending trimming data to fit model or particular distribution pattern.

Hi Rudy, I also suggest you read about Chow test. Thanks Jim for the hint.

Also here: http://en.wikipedia.org/wiki/Prediction

http://en.wikipedia.org/wiki/Forecasting

You're welcome, Eliab. I think that "Prognosis" can be used widely for any diagnostic works as you have suggested in industry and operations, which however is more commonly used by medical doctors. Analogically speaking, detecting machine errors is just like diagnosing human diseases.

Rudy -

As I recently noted to you in an email exchange, I most likely had your question above more in mind when I recently put an answer under the question found at the first link below. I had just posted some notes on my profile as "unpublished notes," with regard to the distinction between 'prediction' for a cross-sectional survey, and an earlier 'forecast' for that period, when used for imputation.

A link to those notes is also attached here.

Thank you - Jim

https://www.researchgate.net/post/What_is_the_difference_between_prediction_and_estimation

Research When Prediction is Not Time Series Forecasting

Prediction is more precise, often involving quantifiable outcome. A forecast is more likely to be a scenario. For example based on predictions of temperature and pressure levels, climatologists arrive at the forecast of weather, which is a set of prevailing parameters (including but not limited to: temperature, pressure) giving a classification of weather such as cloudy, rainy, stormy, sunny. On the economic front, it tends to be the reverse. Predictions, provide a summary description of the position within the business cycle, a forecast may involve the value of an economic metric. Typically whether a composite index will breach some "psychological barrier". So the word "forecast" is more often used compared to "prediction".

Based on a Google Trends search, in the tropics, the word "predict" is often used. Whereas in the temperate zones, the word "forecast" is preferred. It would seem that in an environment of relative stability (in this case, temperature variations in the tropical vs. temperate zones), "predictions" is preferred over "forecasts". So it may be valid to conclude...

"... that forecast involve a probability statement while a prediction is plane hunches of future events based on present circumstances."

http://www.frbsf.org/economic-research/files/wp07-16bk.pdf

Article Should we care? Psychological barriers in stock markets

Even comes the word Estimation. I always got confused of these three terms; forecast, predict and estimate. For me all have time and spatial variability and somehow describe same incident

I was reading alot about the difference between the prediction and forecasting.. I think both are same meaning but their use is different. However, prediction comes from heart (no maths just feelings) while forecast comes from the mind (some science and maths are involved). For example, I predict that their marriage will fail and forecast that they they will have easy settlement with their shared company fortune !!!

Forecasting is the process of making predictions(prediction =Qualitative methods +Quantitative methods., of forecasting ) of the future based on past and present data and most commonly by analysis of trends. Basically there is two types of forecasting Qualitative methods and Quantitative methods.

Qualitative methods are based on judgments, opinions, intuition, emotions, or personal experiences and are subjective in nature. They do not rely on any rigorous mathematical computations.

Quantitative methods are based on mathematical (quantitative) models, and are objective in nature. They rely heavily on mathematical computations. Quantitative methods can be dived in to Time-Series Models and Associative Models, Time series models look at past patterns of data and attempt to predict the future based upon the underlying patterns contained within those data.

In survey statistics, "prediction" refers to regression used for inference for a given population (at a specific point in time).  That is not a time series forecast.  Note the following book title:

Finite Population Sampling and Inference: A Prediction Approach, 2000, Richard Valliant, Alan H. Dorfman, Richard M. Royall, Wiley Series in Probability and Statistics.  

Thus we have prediction intervals for random variable y, and confidence intervals on the independent x variables/predictors/regressors (though actually the independent variables really can influence each other, collinearity for example, messing up the confidence intervals). 

Thus we have observed y-values, predicted-y-values, and the difference for any case where we have both is an estimated residual.  We can estimate the variance of the prediction error for an individual predicted y or predicted total (which would be a sum of observed y from the sample, and predictions for the rest of the population - but the estimated variance of the prediction error regarding the predicted total is not the sum of the estimated variances of the prediction errors for the out-of-sample cases).

I am searching for a paper/book to cite on this issue. @ Amila Shanaka can you recommend one with your explanation? You would help me alot!

I think that forecasting is more specific since it takes into consideration the notion of time. Prediction is a more general term that aim to predict the value of a dependent variable based on independent variables. This independent variable could have or not have a temporal dimension.