Courses 2021

Heavy-tailed and dependent models and robust inference in finance and economics

For whom?

The mini-course is designed for masters , postgraduates, teachers and all persons interested in econometrics.

Course language


The occurrence of economic and financial crises and other structural shocks to markets result in large fluctuations, extreme observations, outliers and heterogeneity. As leading examples, one can mention the beginning of the recent financial crisis that was accompanied by the Dow Jones Industrial Average (DJIA) decline by more than 50% over a period of 17 months, the Black Monday of 19 October 1987 when the DJIA experienced the largest one-day percentage drop of more than 22% and the Flash Crash of 6 May 2010 with the biggest one-day point decline of about 1000 points in the DJIA.

In addition to those stylized facts, financial time series typically exhibit volatility clustering. Large price changes tend to be followed by large price changes, of either sign, a phenomenon that was discovered by Clive Granger and is among the reasons he was awarded a Nobel Prize. In other words, financial time series exhibit non-linear dependence over time: although returns themselves are uncorrelated (that is, returns cannot be predicted using linear functions of the past data), their simple non-linear functions and measures of volatility  display significant (auto-)correlation and dependence.

Further, as demonstrated by the quick spread of the 2008 global crisis, modern markets are very interconnected and affected by financial contagion. Importantly, correlation and interdependence between financial and economic markets is time-varying and considerably increases during the periods of high volatility, financial turmoil and crises.

Heterogeneity, auto-corretaion, dependence and heavy tails considerably complicate empirical analysis. Many standard inference procedures, including least squares regressions and autocorrelation analysis, do not apply directly in the presence of either of those aforementioned stylized. For instance, the widely used standard ordinary least squares  regression methods cannot be used in the case of data generated by heavy-tailed processes with tail indices smaller than two and infinite variances. In less extreme cases, where estimators of parameters of interest remain valid, it usually becomes considerably more challenging to correctly estimate their standard errors.

Heavy-tailedness and dependence are also of critical importance for the properties and robustness of many models in economics, finance, risk management and insurance. In particular, the presence of heavy tails can either reinforce or reverse the implications of a number of important models in these fields. For example, this is the case for the analysis of diversification in Value at Risk (VaR) models: while diversification is preferable for moderately heavy-tailed risks with tail indices greater than one and finite first moments, it becomes suboptimal in the case of extremely heavy-tailed risks with tail indices smaller than one and infinite means. Similar conclusions on (non-)robustness hold for a number of other models in economics and finance, including those of optimal bundling by the multiproduct monopolist, firm growth theory, time series driven by heavy-tailed innovations.

The course will discuss modern approaches to modeling and the analysis of implications of heavy-tailedness, heterogeneity, dependence and contagion in economics and finance. It will also discuss modern approaches to inference on these properties of economic and financial markets, including the degree of heavy-tailedness, probability of crises and dependence structures dealt with. We will further focus on new approaches to robust inference on parameters of economic and financial models (e.g., predictive regressions for financial returns or foreign exchange rates), that are applicable under a wide range of heterogeneity, heavy-tailedness, autocorrelation and dependence properties exhibited by many key economic and financial time series in different economies, including Russia.

Date: September 27 - October 1, 2021


Lectures 1-2.  September 27. Beginning at 16.00.
Introduction. Stylized facts of financial markets: Crises, heavy tails, nonlinear dependence and volatility clustering. Implications of heavy-tailedness and dependence for economic and financial models and standard statistical and econometric methods.

Lectures 3-4. September 28. Beginning at 16.00.
Robust inference under heterogeneity and autocorrelation. Heteroskedasticity and autocorrelation consistent (HAC) standard errors and HAC inference approaches. New approaches to robust inference using t-statistics in group estimators of parameters of interest.

Lectures 5-6. September 29. Beginning at 16.00.
Modern approaches to modeling and inference on heavy-tailedness in economic and financial markets. Empirical results: The likelihood of crises and heavy tails in developed and emerging economies, including Russia.

Lectures 7-8. September 30th. Beginning at 16.00.
Econometric approaches to modeling stylized facts of financial markets and their key time series, including nonlinear dependence, volatility clustering, heavy tails and contagion. Univariate and multivariate GARCH models.

Lectures 9-10. October 1st. Beginning at 16.00.
Modern approaches to modeling contagion and interdependence in financial markerts. Copula models and inference on copula dependence structures. Open research problems. Conclusion.

Readings and course materials:
The slides and research papers on the topics covered will be available on the course website. The following monographs are suggested as useful references:
  • Campbell, J. Y., Lo, A. W. and MacKinlay, M. C. (1997). Econometrics of Financial Markets Princeton University Press.
  • Ibragimov, M., Ibragimov, R. and Walden, J. (2015). Heavy-Tailed Distributions and Robustness in Economics and Finance, Lecture Notes in Statistics 214, Springer
  • Ibragimov, R. and Prokhorov, A. (2017). Heavy Tails and Copulas: Topics in Dependence Modelling in Economics and Finance. World Scientific.
  • McNeil, A. J., Frey, R. and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press.
  • Stock, J. H. and Watson, M. W. (2012). Introduction to Econometrics. 3rd ed., Internat. Global Ed.. Pearson. 
Additional references:
  • Christoffersen, P. F. (2011). Elements of Financial Risk. 2nd ed.. Elsevier Science. 
  • Embrechts, P., Klüppelberg, C., Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer.

Lecturer: Ibragimov Rustam Maratovich - professor, Imperial College London, UK; Chief Researcher, Center for Econometrics and Business Analytics, St. Petersburg State University.

Organizers: L.V. Gadasina (acting head of the Center for Econometrics and Business Analytics), Podkorytova O.A. (senior researcher at the Center for Econometrics and Business Analytics).