Instructor: Giuseppe Cavaliere, Professor of Econometrics, University of Bologna and Distinguished Research Professor of Economics, University of Exeter Business School.
Teaching Assistant (for the Computer Labs): Edoardo Zanelli, PhD Candidate, Department of Economics, University of Bologna.

Course aims and overview

The aim of this course is to provide an up-to-date overview of bootstrap methods for statistical inference, with a specific focus on its application to time series models for economic and financial data. Particular attention will be given to estimation and inference for univariate and multivariate models, both for stationary and non-stationary time series.

This course will introduce students to the theoretical properties of modern bootstrap algorithms as well as guide them in the practical selection of the appropriate bootstrap methodology for the problem of interest. Applications will include macroeconomic models with structural breaks, financial (high-frequency data) and stochastic volatility/GARCH models. At the end of the course, students will possess the tools to assess validity of the bootstrap through theoretical arguments, as well as to construct numerical simulations to show the finite-sample performance of the estimators and tests of interest.

Background

This course is designed for students interested in the recent advances in estimation and inference for Time Series models. Students should have a preliminary background in econometrics and probability theory. While any prior knowledge of time series econometrics and bootstrap methods can be helpful, it is not necessary.

Laboratory sessions will be conducted using MATLAB and will cover: 1) setting up Monte Carlo simulations to assess the performance of the considered estimators/tests; 2) empirical analysis using real-world data. Previous knowledge of the software is not required, as preliminary concepts of programming will be discussed. All codes will be shared with students during the course.

Lecture Outline (tentative)

• Day 1
  • Lecture 1: Introduction to the bootstrap,
  • Lab 1: Introduction to coding on Matlab. Simulations of simple processes.
• Day 2
  • Lecture 2a: Time series models for stationary data.
  • Lecture 2b: The bootstrap for stationary autoregressive models.
  • Lab 2: Evaluation of the performance of estimators/tests through Monte Carlo. Simulation of stationary autoregressions. Applications to fiscal data: inference on fiscal multipliers.
• Day 3
  • Lecture 3a. Non-stationarity in time series models: unit roots and cointegration.
  • Lecture 3b: Bootstrapping non-stationarity time series models.
• Day 4
  • Lecture 4a: Models for volatility and conditional variances.
  • Lecture 4b: Bootstrapping volatility models.
  • Lab 3: Non-stationarity in inflation data and instabilities in the Phillips curve. Monte Carlo simulations of non-stationary autoregressions.
• Day 5
  • Lecture 5: Non-standard applications of the bootstrap.
  • Lab 4: Monte Carlo Analysis of non-standard bootstrap methods. Applications to financial data.