6
$\begingroup$

Rob Hyndman states:

"The paper describing the competition [M] (Makridakis et al, 1982) had a profound effect on forecasting research. It caused researchers to: ... treat forecasting as a different problem from time series analysis"

and

"Even today, I often have to explain to other academics why forecasting is not just an application of time series analysis".

I'd like to get a better understanding of where we draw the line between time series analysis and forecasting. What question is time series analysis trying to answer? What question is forecasting trying to answer? To restrict the scope a bit, let's focus on a single time series and what it would mean to conduct time series analysis on it and what would it mean to forecast it?

Hyndman, R. J. (2020). A brief history of forecasting competitions. International Journal of Forecasting, 36(1), 7–14.

$\endgroup$

1 Answer 1

12
+50
$\begingroup$

Forecasting tries to answer questions like "can we predict the distribution of values of a time series variable at some point in the future?" Consider Sugihara's simplex projection (a kind of state space reconstruction method), which can make reasonable short term forecasts on a time series variable, even when that variable is itself causally linked with other unmeasured variables.

Time series analysis may instead ask questions like "what explains the behavior of variables across time?" Consider Abadie's synthetic control methods as ways of explaining the causal effect of policies on macro-level variables.

Your question gets at the distinctions between explanation and prediction. Really good explanations may not give much predictive power. Really good predictive systems, may even behave as a black box, and provide little to no explanation. In a time series context explanation and prediction are also both domains of concern about uncertainty and inference.

Finally, I would say that, my pointing at distinctions between prediction and explanation aside, "time series analysis" is a broad term, and covers explanatory methods, some people would probably see forecasting as a subset of time series methods, and of course, some people will simply be interested in the behavior of a time series (for example in an AR(1) setting, drawing distinctions between strong and weak stationarity and unit root, moving average errors, behavior of expected values, etc.).

Summarizing, I would say that "time series analysis" broadly encompasses:

  1. Description and categorization of time-series behaviors
  2. Prediction of time-series behavior
  3. Explanation of time-series behavior

I read Hyndman as lauding the attention to #2 that the forecasting competitions were producing, including the critical insight that explanatory (but perhaps also descriptive) time-series models do not necessarily produce wonderful predictions.


References

Abadie, A. (2021). Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects. Journal of Economic Literature, 59(2), 391–425.

Rescher, N. (1958). On Prediction and Explanation. The British Journal for the Philosophy of Science, 8(32), 281–290.

Scheffler, I. (1957). Explanation, Prediction, and Abstraction. The British Journal for the Philosophy of Science, 7(28), 293–309.

Shmueli, G. (2010). To Explain or to Predict? Statistical Science, 25(3), 289–310.

Sugihara, G., & May, R. M. (1990). Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature, 344(6268), 734–741.

$\endgroup$
23
  • 1
    $\begingroup$ @ColorStatistics I think you should have patience with my answer. :) (Although I did just add another edit to it. :) I will see if I can add a few more edits to last last point. $\endgroup$
    – Alexis
    Dec 28, 2021 at 23:18
  • 1
    $\begingroup$ @ColorStatistics I do not disagree that many TS analyses are not causal, but see the first point in my summary. That said, there are plenty of causal time series analysts (that was part of my choice for synthetic control methods, which, granted, are not about a single AR(1) time series :). Sugihara and the empirical dynamic modeling crowd are also making strong claims about the usefulness of their methods for causal inference. Do you mean to ask something like "What is the difference between forecasting and ARCH or ARIMA?" or something like that? $\endgroup$
    – Alexis
    Dec 28, 2021 at 23:33
  • 1
    $\begingroup$ ... Also, you write that "Really good explanations may not give much predictive power." In such cases, I would seriously doubt that the explanation was really that good. Do you have specific examples in mind? In forecasting especially, there is a big danger of us telling stories to ourselves that sound great ("good explanations") but that do not improve the forecast in the least. Often to everyone's consternation. I deal with this effect on a regular basis in talking to customers who are completely convinced that their time series would be better forecasted by including the weather etc. $\endgroup$ Dec 29, 2021 at 15:30
  • 1
    $\begingroup$ 1/2 @StephanKolassa "Really good explanations may not give much predictive power." Absolutely: let's take the Lorenz Curve as an example: it's a purely deterministic time series of three variables in a complex causal network where the value of any variable at some point in time is caused directly or indirectly by previous values of all three variables. $\endgroup$
    – Alexis
    Dec 29, 2021 at 18:23
  • 1
    $\begingroup$ @StephanKolassa I suspect Hyndman wouldn't mind including forecasting as one of the things time series analysis does; from his textbook "we have restricted our focus to time series forecasting… all forecasting… concerns prediction of data at future times using observations collected in the past." I also suspect that there is some semantic blurriness about what gets called time series analysis. Like, some canonize a finite set of ARIMA, VAR, etc. models as "time series analysis," while some are comfy calling analysis of time series data (inc. forecasts) "time series analysis". $\endgroup$
    – Alexis
    Dec 31, 2021 at 0:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.