Forecasting vs Classification In the context of time series, can classification be considered a sub-type of forecasting? I feel like classification is simply projecting the outcome of a certain data set onto a predefined group of outcomes, which sounds similar to forecasting.
 A: I don't really think this is a useful way of looking at things.


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*For instance, you could classify time series as "seasonal" versus "non-seasonal" - but this classification, by itself, won't tell you whether you are looking at ice cream (high sales in summer) or snow shovels (high sales in winter).

*Even if your classification is more fine-grained and classifies a given time series as "seasonal, with high sales in summer", your forecast would still depend on whether you are forecasting for summer or for winter.

*Same problem if you classify as "trended" versus "non-trended".

*If your classification involves finding the orders of an ARMA model, you still need to estimate the parameters. (And to know how far out you want to forecast.)
I would not say that time series classification involves "projecting the outcome of a certain data set onto a predefined group of outcomes". I think the term "outcomes" is misleading here. In my view, time series classification is more about detecting features in time series, like the ones discussed above. These can then help you to choose and estimate an appropriate model (or multiple ones, for forecast combination), so you don't forecast an obviously seasonal series using a non-seasonal model. But you still need to fit that model and extrapolate.
A: 
I feel like classification is simply projecting the outcome of a certain data set onto a predefined group of outcomes, which sounds similar to forecasting.

After all you may forecast tomorrow's temperature as (38 degrees C), and you can also forecast tomorrow's temperature as hot (meaning >37 degrees c). Both are forecasts because they are predictions about the future.

The general flaw in these arguments is that classification is not about classifying the future outcome of some variable or future values or episodes of some time series but about classifying what you already have. Of course such a classification means that you expect the classification to hold in the future as well, but you would have to stretch your definition of forecast a lot to include this and it also misses the point of classification entirely.
A few examples to illustrate this:


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*Suppose you measure some time series that can fall in one of the two following classes:


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*All values are independently drawn from a normal distribution with mean 0 and standard deviation 1.

*All values are independently drawn from a uniform distribution with mean 5 and standard deviation 2.


As the time series have no memory, you cannot make any predictive statement other than about the general distribution of the time series’s values. However, recording some values, you can assign a time series to one of the above classes. So classification is possible, while forecasting isn’t.

*Suppose you measure some time series that can fall in one of the two following classes:


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*Values generated by a chaotic map (e.g., the logistic map).

*All values are independently drawn from the distribution of values of the same map.


Again, you cannot possibly forecast time series of the second type, but you can for the first type. Classifying your time series with the above classes thus makes a statement about the applicability of forecasting procedures, but it is not forecasting itself.

*Finally, a practical example. Before performing epilepsy surgery, you record EEGs of the patient at several points on or in the brain. You then try to classify the resulting time series (preferrably during a seizure) to find out which time series comes from a region of the brain that is relevant to the seizures. This classification does not allow you to perform any type of forecasting: You cannot say when the patient will have seizures (seizure prediction is notoriously difficult), and you already know that the patient has seizures. However, you can use your insights from the classification to alter the system by removing or disconnecting a responsible part of the brain. So, in this example, there is classification but no forecast whatsoever.
A: I believe so. After all you may forecast tomorrow's temperature as (38 degrees C), and you can also forecast tomorrow's temperature as hot (meaning >37 degrees c). Both are forecasts because they are predictions about the future.
