Bootstrap Methods for Time-Varying Processes


The properties of many economic time series vary over time, as our economy is continually evolving. Reliable inference on time-varying processes is therefore of paramount importance. The objective of this proposal is to develop bootstrap methods that allow for reliable inference on such time-varying processes. The bootstrap has advantages over standard asymptotic inference: it is often more accurate in properly specified models, and more robust in mis-specified models. In non-standard settings with time-varying processes asymptotic inference is often not accurate, and may not even be available, so the bootstrap is a natural alternative. However, traditional bootstrap methods are also not valid in such non-standard settings. I will therefore develop new bootstrap approaches for a number of settings characterized by time-varying processes. These methods allow for inference on certain aspects of change and offer robustness to other aspects of change that are not central to the interests of the researcher.

The proposal consists of three parts. Level changes in the form of trends are the subject of the first two parts. In part I, inference on common stochastic trends (cointegration), such as found in macro-economics, is considered. Deterministic trends, important in economics of growth and climatology, are considered in part II. The analysis considers both linear and nonlinear trends. In both parts bootstrap methods will be developed that are robust to time-varying volatility. Part III considers changes in variance through inference on time-varying volatility using high-frequency data. The focus is on allowing for and testing for the presence of jumps, which is important for financial applications. Throughout all parts bootstrap methods are developed that improve on existing techniques. The methods are analyzed theoretically, in particular to establish their asymptotic validity, through simulations and via applications.


Scientific article

  • S Smeekes(2015): Bootstrap sequential tests to determine the order of integration of individual units in a time series panel Journal of Time Series Analysis pp. 398 - 415 ISSN: 1467-9892.
  • G Cavaliere, PCB Phillips, S Smeekes, AMR Taylor(2015): Lag length selection for unit root tests in the presence of nonstationary volatility Econometric Reviews pp. 512 - 536 ISSN: 1532-4168.
  • S Smeekes, TB Götz, A Hecq(2016): Testing for Granger Causality in Large Mixed-Frequency VARs Journal of Econometrics pp. 418 - 432
  • C Hurlin, S Laurent, R Quaedvlieg, S Smeekes(2017): Risk Measure Inference Journal of Business & Economic Statistics pp. 499 - 512

Professional publication

Publications for the general public

  • J Urbain, S Smeekes(2013): A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing
  • S Smeekes, J Westerlund(2014): Robust block bootstrap panel predictability tests
  • L Lieb, S Smeekes(2015): Bootstrap inference for VAR models under rank uncertainty


Project number


Main applicant

Dr. S.J.M. Smeekes

Affiliated with

Maastricht University, School of Business and Economics (SBE), Department of Quantitative Economics

Team members

Dr. S.J.M. Smeekes


01/02/2013 to 31/01/2016