Is time series analysis a saturated field?

Question

I have had some experience with conventional time series analysis models (ARMA ARCH GARCH etc) in the past.

While I find it very useful it appears to me that there are no open directions to the field. While the equations are being applied for modeling and prediction they are usually just compared to state of the art tools (such as neural nets, support vector machines etc).

Is that incorrect? If so what are the main frontiers in which the time series analysis is expanding? Are there big questions that need to be addressed?

Answer 1

I don't have a huge amount of experience here but I did an undergraduate-level thesis on time series models like ARCH/GARCH and ARMA. At the time, it was new and exciting to study the limiting case as the time interval tended to $0$, leading to continuous-time stochastic processes (including the COGARCH model in some cases). After looking at some recent papers, it seems that there is still a lot left to understand regarding what happens when $\Delta t \rightarrow 0$ and that this is an active area of research.

This is just an example - by all means there are other things to study. Time series analysis is still an active field.

Answer 2

I understand your point but I think there are a lot of open and interesting questions that are being explored in the field.

One problem with cutting-edge tools like neural nets and deep learning is that they are black box models. For instance If you use an AR(2) model to predict a dataset and you find using the auto_arima functions in python that

$$x_t = 0.5 x_{t-1} - 0.1 x_{t-2} + \varepsilon_t$$ you understand inmediatly that $x_t$ is affected positively by its antecesor $x_t$ and negatively by the value two instances before.

This is a simple model (perhaps too simple). If you use a neural net you may find that under the current data it has a lower error (for instance MAE) but you can not elaborate an analysis as the one we did before. In other words you lose interpretability.

Regarding your concerns about the possibility of no open directions to the field I would encourage you to take a look in the advances in the field of irregular time series. This is a relatively new topic that arises when the values of the time series are not regularly measured. I think it is a very interesting problem with lots of applications in which the conventional approaches (ARIMA, neural nets...) tend to fail.

Here you have a description:

• https://en.wikipedia.org/wiki/Unevenly_spaced_time_series

Take a look at this paper where the authors adapt granger causality for this type of series:

• Granger Causality Analysis in Irregular Time Series.Taha BahadoriYan LiuYan Liu. https://www.researchgate.net/publication/265624354_Granger_Causality_Analysis_in_Irregular_Time_Series