The course is divided into two parts: the first one, devoted to time series and the second one to econometric analysis of qualitative response models (notably LOGIT and PROBIT models), risk measures and copulas. Each time, the developments range from theory to applications, with practical implementations using R/Python (course of Quantitative Finance).

This course is devoted to times series: first, taken separately, with the treatment of non-stationarity (Unit root) and heteroskedasticity (ARCH effects), second, in a multivariate approach, with standard linear models (VAR models and VECM ones in case of cointegration) and an introduction to non-linear ones (smooth transition regression, STR). An extension is then presented to deal with learning of the dynamics of complex systems involving networks.

1.1  AR(I)MA models & Unit root (review) (Session 1&2)

1.2  Introduction to ARCH models (review) (Session 2)

1.3  Introduction to non-linear models: the case of STR models (Session 3)

1.4 Multivariate systems (Session 4&5)

VAR models (review)

Cointegration and VEC models

1.5 Dynamic networks including VAR models (Session 6)

Bibliography 

Ahelegbey, D.F., Billio, M., and R. Casarin, 2015, Bayesian Graphical Models for Structural Vector Autoregressive Processes,” Journal of Applied Econometrics.

Banerjee, Dolado, Galbraith et Hendry, 1993, Cointegration, Error Correction and the Econometric Analysis of Non-stationary Data, Oxford.

Engle, R.F. and D.L McFaden, ed. Handbook of Econometrics, vol.4, pp.2843-2915.

Engle, R.F. 1982 , Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation , Econometrica , Vol. 50, No. 4 (Jul., 1982), pp. 987-1007.

Gonzalez-Rivera, G., 1998, Smooth-Transition GARCH Models, in Studies in Nonlinear Dynamics and Econometrics, Quarterly Journal Volume 3, Number 2, The MIT Press.

Granger, C. W. and T. Teräsvirta, 1993, Modelling non-linear economic relationships, Oxford University Press.

Hamilton, J. « Time Series Analysis », Princeton University Press.

Luis M. Lopez-Ramos, L.M., Romero, D. Zaman, B. and B. Beferull-Lozano, 2018, Dynamic Network identification from non-stationarity vector autoregressive time series, https://arxiv.org/abs/1807.02013, Cornwell University Library.

Lütkepohl, H., 1990, Introduction to Multiple Time Series Analysis," Springer Verlag, New-York.

Teräsvirta, T., 1996,  « Modelling economic relationships with smooth transition regressions Handbook of Applied Economic Statistics, edited by David  Giles and Aman Ullah.

UNIT ROOT TESTS https://faculty.washington.edu/ezivot/econ584/notes/unitroot.pdf

COINTEGRATION Lecture: Introduction to Cointegration - Applied Econometricsstaff.utia.cas.cz/barunik/files/appliedecono/Lecture7.pdf

ARCH-TYPE MODELS  Introduction to ARCH Models — arch 4.4.1+9.g0c6b035 documentation

This course addresses three main issues:

- Credit scoring with the classical PROBIT and LOGIT models, extended in order to deal with big data by using machine learning and neural networks

- Risk measures (Value at Risk and Expected shortfall), first, with their standard use for regulation purposes and, second, in connection with networks to capture systemic risk

- Copulas with applications to portfolio management and extensions with Bayesian networks to deal with high dimensional systems, notably to assess contagion of extreme risks.

1.      Qualitative response models (2 sessions)

1.1 Standard econometric approach (PROBIT and LOGIT models)

1.2 Neural networks and credit scoring with Perceptron convergence procedure and Backpropagation Learning Algorithm.

Bibliography 

Bart, 2013,  Using neural networks for credit scoring: a simple example,

https://www.r-bloggers.com/using-neural-networks-for-credit-scoring-a-simple-example/

Comelli, F., 2014, Comparing the Performance of Logit and Probit Early Warning Systems for Currency Crises in Emerging Market Economies , IMF working Paper WP/14/65.

Halloran, S.O Lecture 9: Logit/Probit

www.columbia.edu/~so33/SusDev/Lecture_9.pdf

Moore, C. « An Introduction to Logistic and Probit Regression Models »

https://liberalarts.utexas.edu/.../Fall2013_Moore_Logistic_Probit_Regression

Tam, K.Y.  and M. Y. Kiang 1992, MANAGERIAL APPLICATIONS OF NEURAL NETWORKS: THE CASE OF BANK FAILURE PREDICTIONS », Management Science, Vol. 38, N° 7.

West, D. , 2000, Neural network credit scoring models , Computers & Operations Research, Volume 27, Issues 11–12, 1131-1152.

2.      Risk measures (2 sessions)

2.1 Value at risk

2.2 Expected shortfall

2.3 Coherent measures

2.4 Systemic risk measures for Network models

Bibliography 

Jorion, P., 2007, Value at Risk: The New Benchmark for Managing Financial Risk, McGraw Hill.

McNeil, A. J.  Frey, R.  and P. Embrechts, 2005, Quantitative Risk Management: Concepts, Techniques and Tools., Princeton University Press.

Silva, T.C., Guerra, S. M., da Silva, M.A. and B. M. Tabak, Measuring Systemic Risk under Monetary Policy Shocks: a network approach

http://web.abo.fi/fak/mnf/mate/tammerfors08/embrechts_tuesday.pdf

CRAN - Package NetworkRiskMeasures

3. Copulas’ theory (2 sessions)

3.1 Introduction

4.2 Copulas and Machine learning

Bibliography 

Bouyé, E. 2000,  Copulas for Finance A Reading Guide and Some Applications », www.thierry-roncalli.com/download/copula-survey.pdf

Elidan, G., 2010, Copula Bayesian networks. In: Neural Info. Processing Systems (NIPS.)

Elidan, G., 2010, Inference-less density estimation using copula bayesian networks, in « Uncertainty in Artificial Intelligence (UAI) » . Rachev, S.T.,  Stein, M. and Sun, W. , Copula Concepts in Financial Markets - KIT statistik.econ.kit.edu/.../Copula_Concepts_in_Financial_Markets

Segers, J., 2013, Copulas: An Introduction I - Fundamentals - Columbia University