I can only talk about quantitative trading. As a rule of thumb, the lower frequency you work in, the more econometrics is important, whereas for a higher frequency, the more econometrics becomes useless. (I would still recommend a top econometrician for HFT since they have what it takes to succeed, it's just the models aren't out-of-the-box applicable.)
But if I was interviewing someone who was educated in econometrics for a quantitative research position, I would hope for (given the relevance to financial time-series):
I have tried to put in a legend, ^ is something you should learn later and ^^ is something you should learn after learning ^.
- ^^ Kalman filters for dynamic linear models.
- GARCH (learn ARCH first).
- Econometric forecast evaluation (RMSE,MSE,MAE).
- Thorough OLS understanding. Assumptions and consequences of violation.
- ^ Regime switching and threshold models.
- Cointegration models such as VECM and Engle-Granger and basic $I(n)$ theory along with ADF/PP unit root testing.
- ^ Quantile regression.
- Basic knowledge of dimensionality reduction algorithms (the more the better, but I wouldn't have this as an expectation for an econometrics candidate).
- ^ Impulse response functions.
- ^ Monte carlo applications to construct sampling distributions and the idea of the bootstrap, along with general knowledge of at least one bootstrap estimator.
- A good knowledge of hypothesis testing, sampling distributions, population/sample concepts, lag length selection, consistency/power/bias, variance/bias tradeoff, maximum likelihood, PDF/CDF, qualitative knowledge of different distributions commonly used.
- A knowledge of why and how econometricians pre-process data, take differences, introduce variables and account for non-linearities with simple transforms on the individual features, interactions between features, ratios of features and indicator function breaks (either data determined or, usually more appropriately, determined a priori).
- Comovement not necessarily as a slope phenomenon; linear correlations (and its pitfalls), rank correlations, three-way relationship between correlation, linear regression slope and cointegrating vector, how to test for spillovers in a linear DGP, and more global and advanced dependence estimators (such as copula, wavelet, mutual information, IRFs through VECM/VAR, forecast error variance decompositions, among others).
- The difference between residual analysis and test set cross-validation, and how both relate to overfitting and model generalisation.
I would not care about:
I would also like to see hopefully (most likely picked up from self-study):
- ^^ Wavelets (DWT/CWT/phase difference analysis/frequency-domain bivariate correlation) and STFT should be a part of an econometricians toolbox.
- ^^ Dynamic correlation estimators (DCC-GARCH, stochastic copulas)
- A knowledge of generalization theory picked up from machine learning lectures.
- ^^ Methods like NNG to get better OLS estimates. Boosting and bagging linear DGPs for better generalisation.
- ^^ Perpendicular regression and LAD estimators when least squares is not appropriate given some assumption violation, if the conditional expectation is not wanted (conditional median is theoretically desirable), or if you don't want to inadvertently do least-rectangles upon a misspecification of the causal relationship, or you want the loss to be less skewed by outliers.
Here is some voluntary stuff that either I have seen some top guys working on in industry or in an econometrics paper, and I would be very impressed to see knowledge in these areas:
- Stochastic optimal control (a large quantitative global macro fund is doing work on this)
- Bayesian time-series (a reputable, large systematic fund had some research on this)
- I would like to see knowledge of how to come up with a DGP and figure out how to estimate it with numerical methods. As an example, how to embed exogenous variables in the forcing equation in Patton's symmetrized Joe-Clayton copula, then figure out how to optimize the density numerically and bootstrap unbiased and consistent standard errors. Another would be to derive a Kalman estimator to extract time-varying yield curve parameters (curvature, slope, etc). Everyone is estimating simple MGARCH and VECM models since you can just plug the data into
R, so it is doubtful there is alpha here. Probably there is some alpha for the guys that can estimate parsimonious models that others simply can not because they are not in the top 1% of econometricians.
Here is some stuff that's probably not needed in low frequency quantitative research:
- Advanced optimisation theory. GAs, stochastic gradient descient and Newton's are all you will be expected to know.
- Non-linear machine learning.
- Non-linear dimensionality reduction or manifold learning. All you are expected to know is PCA, ICA and the concept of the time-series factor model.
- Digital signal processing not related to comovement estimators.
There is one thing from another field that may be required:
- Ornstein-Uhlenbeck SDEs for a pairs trading fund.
You'll notice I've listed almost all the mainstream stuff that's applicable to time-series. So most of what you'll get in a financial time-series course is what would be the expectation I think.
Note that I did not list high frequency econometrics models, since I think they are not useful in high frequency finance. If you are going for such a position you will be interviewed by computer scientists and electrical engineers who will more likely ask you a question about asymptotic time complexity than about econometrics.