I received the following one-sentence email from a Ph.D. statistician who works in finance:
For every one time I use stochastic calculus I use statistics 99 times.
Not that stochastic calculus isn’t important…after all, I go to the bathroom more often than I use statistics, but that doesn’t mean we need Ph.D. courses in pooping…but still, it says something, I think.
More generally, I think it illustrates that certain application areas (e.g., finance) can get overly attached in the curriculum to certain methods (e.g., stochastic calculus). Another example is economics and time series. Really, I think time series are as important in ecology, political science, and many other fields, as in economics. But for some historical reasons, the econ students tend to learn a lot more time series and the students in other fields tend to learn less.
I couldn't agree more… I spent a couple years studying SDEs & stochastic control in math grad school before switching to a finance Ph.D. program. Almost all the math I do now at work is time-series econometrics. I can barely remember the last time I even wrote and SDE down, much less solved one.
"But for some historical reasons, the econ students tend to learn a lot more time series and the students in other fields tend to learn less." Which group do you think is following the non-optimal path?
Hmm . . . I suppose the optimal path depends on the student. My current belief is that it's not that crucial what statistical method you learn, if you learn some statistical method and how to apply it. Or, to put it another way, whatever tools you have, you'll tend to use them up to, and beyond, their limit, and then you'll need to learn some new tools.
But I do think there should be a continuous connection between the probability theory you learn, and the theoretical statistics, and the applied statistics, and the quantitative social-science modeling. I don't think classical asymptotics does that, and I also have never understood the idea that a "unit root test" can tall me much about a social process. I prefer methods where you can build the statistical model to describe the data as closely as possible.
That said, we should all probably be doing more hierarchical time series modeling. Probably not the ARMA etc. stuff, though.
I had a class in time series in Industrial Engineering (after transferring from biostatistics). The IE professor loved really high-order ARIMA models (e.g., 15, 15). That was the only method that he taught. For his applications (control problems in machining), it made sense, and he did some useful work. However, the engineering students who didn't know anything else were disserved.