A time-varying parameter model for local explosions

Francisco Blasques, Siem Jan Koopman*, Marc Nientker

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

76 Downloads (Pure)


Financial and economic time series can feature locally explosive behaviour when bubbles are formed. We develop a time-varying parameter model that is capable of describing this behaviour in time series data. Our proposed dynamic model can be used to predict the emergence, existence and burst of bubbles. We adopt a flexible observation driven model specification that allows for different bubble shapes and behaviour. We establish stationarity, ergodicity, and bounded moments of the data generated by our model. Furthermore, we obtain the consistency and asymptotic normality of the maximum likelihood estimator. Given the parameter estimates in the model, the implied filter is capable of extracting the unobserved bubble process from the observed data. We study finite-sample properties of our estimator through a Monte Carlo simulation study. Finally, we show that our model compares well with existing noncausal models in a financial application concerning the Bitcoin/US dollar exchange rate.

Original languageEnglish
Pages (from-to)65-84
Number of pages20
JournalJournal of Econometrics
Issue number1
Publication statusPublished - Mar 2022

Bibliographical note

Funding Information:
Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099 ) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation , ( DNRF78 ).

Publisher Copyright:
© 2021 Elsevier B.V.


  • Asymptotic normality
  • Consistency
  • Explosive processes
  • Invertibility
  • Speculative bubble


Dive into the research topics of 'A time-varying parameter model for local explosions'. Together they form a unique fingerprint.

Cite this