Principles, ideas and theory in econometric time series

With examples from cointegration, bootstrap, ARCH, state space and big data models

Bertinoro, 17 - 22 June 2019



Juri Marcucci
Bank of Italy
Via Nazionale 91, 00184 Rome, Italy




Basic Requirements

Intermediate knowledge of econometrics

Course outline

The course will be in two main parts: The first part discusses econometric methods and theory, which are applied in the second part, where selected topics from cointegration, statespace models, the bootstrap and multivariate ARCH models, as well as big data modelling will be discussed in detail from recent research.

Course description:

In Part I, we give an introduction, aimed for graduate/Ph.D. level students in econo-metrics, to (i) asymptotic theory for stationary, i.i.d. as well as non-stationary (integrated of order one) variables; (ii) theory for the bootstrap; (iii) theory for cointegration and for(multivariate) ARCH models; and, (iv) theory for the Kalman filter. All theory presented will be in terms of examples where details are explained, rather than providing a general introduction to the field(s).

In Part II, we discuss recent research with reference to the theory and methodology introduced in Part I.

The topics include:

  • Cointegration and adjustment in a common trends causal model and the role of weakexogeneity.
  • Optimal hedging and cointegration in the presence of heteroscedastic errors.
  • Bootstrap based inference in stationary and non-stationary (conditionally heteroscedas-tic) autoregressive models.
  • Models, Methods and Big Data


  • Jensen, S.T. and A. Rahbek (2004), Asymptotic Inference for Nonstationary GARCH, Econometric Theory,20:1203ñ1226.
  • Johansen, S. and A. Rahbek (2019), Lecture notes, unpublished.
  • Kristensen, D. and A. Rahbek (2005), Asymptotics of the QMLE for a Class of ARCH(q) Models, Econometric Theory,21:946-961.
  • Kristensen, D. and A. Rahbek (2010), Likelihood-based Inference for Cointegration with Nonlinear Error-Correction, Journal of Econometrics,158:78-94
  • Cavaliere, G. and A. Rahbek (2012), Bootstrap Determination of the Co-IntegrationRank in Vector Autoregressive Models, Econometrica, 80:1721-1740.
  • Cavaliere, G., H.B. Nielsen and A. Rahbek (2017), On the Consisteny of the BootstrapTesting for a Parameter on the Boundary of the Parameter Space,Journal of Time Series Analysis, 38:513-534.
  • Johansen, S. (2018) Inference in a simple nonstationary state space model. Unpublished
  • Chang, Y., J. I. Miller, and J. Y. Park (2009) Extracting a common stochastic trend:Theory with some applications.Journal of Econometrics, 150, 231-247
  • Johansen, S. (2019) Cointegration and Adjustment in the inÖnite order CVAR representation of some partially observed CVAR(1) models, Econometrics, 7:2.
  • Gatarek, L. and Johansen, S. (2019), The role of cointegration for optimal hedging withheteroscedastic error term.Unpublished
  • Cavaliere and Rahbek, Econometric Theory Lecture 2019, Lecce, Italy, unpublished
  • Onatski, A. and C. Wang. (2018), Alternative asymptotics for in cointegration tests inlarge VARs,Econometrica, Vol. 86, No. 4, 1465-1478
  • Chris Anderson (2008), The end of theory: The data deluge makes the scientific method obsolete.Wired Magazine.
  • Chang, Y., C. Kim, and J. Park (2016). Nonstationarity in time series of state densities. Journal of Econometrics,192:152-167.
  • Beare, B. and W. Seo (2018). Representation of I(1) and I(2) autoregressive Hilbertian processes. In press.
  • Franchi, M. and Paruolo, P. (2018) Cointegration in functional autoregressive processes.In press.


Venue and timetables

The Module will last one week and will be held in the University Residential Centre, Via Frangipane 6, 47032 Bertinoro (FC). Participants will be hosted in the Centre guest quarters, (as an exception, in case of reduced availability of rooms in the Centre, they will be accommodated in local hotels).

Lectures and tutorials will be in English, with the following schedule:

Monday to Friday: lectures 9:00-13:00, 15:00-17:00; tutorials and individual hands-on sessions: 17:00-19:00.

Saturday: lectures 9:00-13:00


Fees and Enrollment

  •  Students, PhD students and temporary university staff: 850€
  •  University staff: 1000€ 
  •  Others: 2500€

Fee includes: accommodation (usually in doube room) with breakfast and lunch starting from Sunday evening.

Application deadline   MAY 30th 2019
Fees Payment deadline   June 15th 2019

Programs are conditional to the recruitment of a minimum of 15 participants