A time-varying parameter model for local explosions

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 in data. Our proposed dynamic be used to predict the emergence, existence burst bubbles. adopt flexible observation driven specification allows for different bubble shapes behaviour. establish stationarity, ergodicity, bounded moments data generated by our model. Furthermore, we obtain consistency asymptotic normality maximum likelihood estimator. Given estimates model, implied filter extracting unobserved process from observed study finite-sample properties estimator through Monte Carlo simulation study. Finally, show compares well with existing noncausal models financial application concerning Bitcoin/US dollar exchange rate.