Math help: PDE or Complex Variables?

[econandon]

Originally Posted by puecon

I wonder about this too. I want more specifics. If all you need is to know just some manipulation of complex functions like say sine or exponential then that does not justify taking a potentially very difficult math course. For that, just read the first two chapters of a complex analysis text. On the other hand, if working in time series requires understanding of something like Cauchy's Theorem, then perhaps taking this course could be justified. (I somehow doubt though). You certainly don't need complex analysis to _take_ a time series course and do time series analysis of your data.

Regarding PDEs, this course is probably nice to have for general math/calculus knowledge, but still not required even for asset pricing people. My understanding is that you need to solve PDEs in order to do things like pricing the actual derivative securities, e.g. a very practical applied math question. (BUT WHY would economists POSSIBLY want to do something like that? :-)

I agree, these courses are not really that important. But given a choice between the two, I would say econometric theory or micro/macro theory have some applications. If you are more interested in theory, PDE is a better choice. I don't know exactly what for, I just know a student who is studying PDEs for their dissertation in micro theory. Something about endogenous preferences are given as a PDE. Complex variables are used in spectral theory, and if you are interested in time series this may be useful.

[Internationalstudent08]

If you are equally interested in the two fields and if they are equally difficult, I would go for pde, because it's slightly more useful.

However, I think that their signal value is the same (or even less- it seems to me that pde classes are easier than complex analysis) and... c'mon, the practical usefulness should be the last criterion here. you can do well even without a class on pde

[can_econ]

Originally Posted by treblekicker

Not that I am questioning you, but I am just wondering how complex analysis is used for in time-series.

(Preface: I've never taken a course in complex analysis but) the spectral density function (which is apparently a Fourier transform) is used heavily in some of time-series analysis we're learning in a 1st year class... I assume people doing research in the area need to know this stuff at a higher level (an econometrician in undergrad recommended a course in complex analysis, so it's probably useful for something). So it's probably more useful a class on average for someone wanting to do econometrics than is PDEs (not sure how PDEs are used in econ outside of theory, finance, and math-econ). Except for the basics of complex variables I highly doubt either class would be useful until you were into the dissertation stage, specializing in some specific topic that uses this sort of math.

[Trapped In an EW Box]

Great - thanks, this is really helpful. I'm not looking for signalling value, just looking for which classes I can squeeze in for my last quarter to prepare for the PhD and what would be the best use of my time!

So it seems like the consensus is on PDEs then? Though maybe a statistics course might be more useful? There's a course at my school on causal inference - of course at the exact same time - so I would have to choose between them. How advanced of a statistics background is "good" before entering a program?

[doubtful]

Mathematical Statistics or Estimation Theory might be useful as well.

[Connemara Pony]

DONT DO COMPLEX VARIABLES

I did complex analysis last year, it was the worst course I have ever done in my entire life(and the only C i ever got in college) It's also not relevant. Don't, just don't.

It was so bad that every time I see a complex number I shudder!

[bscout]

Complex Variables are used in some areas of Macro Theory and Asset Pricing models. For instance, to prove that a solution can be written as a polynomial you have to prove Analicity. If you use reals, it take you 20 pages to prove it but if you work in the complex field, it takes you two lines (see Calin, Chen and Cosimano [Econometrica, 2005]). Furthermore, almost any time that you want to write a solution of a economic problem as a polynomial you should prove Analicity...

IMHO, PDE is easier to learn by yourself but as always, it will depend on your interests.

[never6669]

For those in time series, I don't understand why you wouldn't want complex analysis. It is probably overboard in many cases, but all math classes are...

That's why they are math classes and not economics courses. They give us tools to use when it comes to finding our own way to answer unique economic problems.

Euler's method and the fundamental theorem of algebra are the simplest examples I can think of as to why complex analysis is important in time series.