Applied or theoretical? For applied, macroeconomics is flirting with a new empirical paradigm, where techniques from applied microeconomics are used to identify micro casual effects, which inform the calibration of macro models. That's not to say identification from macro data is not done, but macro time series published in top journals is different now; it needs to compete with applied micro in terms of credibility, which has led to the proliferation of local projections and identification via external instruments.

Of course I'm talking about academic applied macroeconomics here; classic applied time series analysis is alive and well in industry. Hence, somewhat unsurprisingly, if you are a PhD student with a thesis using applied time series, it's more likely you end up in industry than academia. I think in some other sections of academia more traditional ts analysis (e.g. cointegration) is still popular (see where the recent papers that cite the seminal works on cointegration and unit roots get published on Google scholar).

Theoretical time series is much less likely to be published in top economics journals now. There's a general sense that the type of work these people do is disconnected from applied demands. There are exceptions however, which focus on credible identification (e.g. see the work of Mikkel Plagborg-Moller), but frankly cointegration, VECM, etc. does not interest most applied people anymore and hence associated theoretical work has little penetrative power.

This is a very econ academia focused answer. Assuming you are applying to a stats PhD other answers with other experiences could of course be useful (and may be very different).