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It seems quants increasingly use econometric models at work. As someone who has sold his soul to probability theory and stochastical analysis I would like to catch up.

What are the econometric tools a quant should be able to wield ?

As I see it, the answer will be highly dependant on where one works. Thus perhaps it would make sense to distinguish:

  • Buy side
  • Sell side
  • Fixed Income
  • Equity
  • Risk Management and Model Validation

Book suggestions that cover the necessary knowledge will be appreciated. Also, if someone feels like it, a list of topics (e.g. ARCH, GARCH etc.) would also be very helpful.

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up vote 23 down vote accepted

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).
  • ARMA(p,q)/ARIMA(p,i,q)/AR(p)/MA(q).
  • 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.
  • VARs.
  • ^ 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:

  • Panel modelling.

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.

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I can unfortunately upvote it only once. Amazing answer and an amazingly long to do list. Could you perhaps explain in which order one should approach this - OLS will be first but what comes aftewards ? (any book suggestions ?) – Probilitator Feb 27 '14 at 13:49
In a "normal" quant job I will have to be equally strong in econometrics and numercs - correct ? – Probilitator Feb 27 '14 at 13:52
I think a mis-edit happened somewhere. Please check mine. – Bob Jansen Feb 27 '14 at 13:52
I think that's a good list (though I never really used wavelets myself). I would add missing, mixed frequency, and irregular data as some issues that I'm constantly either dealing with or begrudgingly ignoring. Seasonal adjustment is important too for some types of analysis (like electricity futures), but I might combine that with the ARMA stuff. I would say that the reason not to focus too much on Panel Modelling is that you'd probably get stuck trying to remember random or fixed effects when instead you should just ignore those and read Gelman's Bayesian Data Analysis. – John Feb 27 '14 at 18:02
@John why not write this comment as an answer - I think it has added value but it will be hard to notice being so far down in the commentaries ;) – Probilitator Feb 27 '14 at 18:43

@user2763361 has a very thorough list of useful econometric topics for quantitative finance.

I would add missing, mixed frequency, and irregular data as major issues that I'm either constantly dealing with or begrudgingly ignoring. Seasonal adjustment is important too for some data (like electricity futures), though the subject is also related to his mention of ARMA models.

He might be right on recommending not to focus too much on Panel Modelling. My recollection of graduate school econometrics was constantly trying to remember whether to use random or fixed effects. I think it had to do a) the frequentist approach to Panel analysis and b) my class' focus on labor market analysis instead of the topics I may have found more useful. Nevertheless, while analyzing Panel data is less important than many of the other topics, that does not mean it has no place in Quantitative Finance. I have found a lot of value reading the literature on hierarchical and multi-level modelling. Hence, I strongly recommend Gelman's Bayesian Data Analysis. At a minimum, it will cure you from thinking about random versus fixed effects.

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Agreed with everything here. Also seasonal adjustment could be modeled with Kalman filters too (the book that goes with the R package dlm is fantastic on this topic). Wavelets are also good for any seasonal stuff (i.e. you could band pass out frequency-domain seasonality if you wanted to, among other things) depending on the application. Also worthwhile to look at the well established central bank models for de-seasonalizing (is that a word?) macro series (eg TRAMO/SEATS) – user2763361 Feb 28 '14 at 12:54
Census X12-ARIMA is also pretty popular for de-seasonalizing also. – John Feb 28 '14 at 16:00

As an overview, Expected Returns, by Antti Ilmanen, was recommended to me. He has a preference for data over theory, so it will appeal to quants. The book is longish, and got a bit heavy at times, but he covers all the investment products and all styles of investing.

The biggest problem might be that it is now 3 years old, and was heavily influenced by events in 2007/2008. I wonder if the author is working on a 2nd edition...

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