# 18-088/III (2018-11-16)

Author(s)
Francisco (F.) Blasques, VU Amsterdam; Siem Jan (S.J.) Koopman, VU Amsterdam; Marc Nientker, VU Amsterdam
Keywords:
bubbles, observation driven models, noncausal models, stationary, ergodic, consistency, asymptotic normality, exchange rates
JEL codes:
C22, C58, G10

Locally explosive behavior is observed in many economic and financial time series when bubbles are formed. We introduce a time-varying parameter model that is capable of describing this behavior in time series data. Our proposed 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 behavior. 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, our filter is capable of extracting the unobserved bubble process from 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 noncausal models in a financial application concerning the Bitcoin/US dollar exchange rate.