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Title: Seasonal bubbles and volatility models Authors:  Tomas del Barrio Castro - University of the Balearic Islands (Spain) [presenting]
Alain Hecq - Maastricht University (Netherlands)
Sean Telg - Maastricht University (Netherlands)
Abstract: Economic and financial bubbles usually emerge when prices strongly exceed the asset's intrinsic value namely the fundamental price. The reasons explaining this phenomenon are many (speculation, excessive monetary liquidity, moral hazard, extrapolation, etc.) and economic history is full of extraordinary examples from the Tulipomania to the more recent Brazilian inflation in the 80's, the, Bitcoin or the subprime crisis. The existence of a bubble is often evaluated retrospect however, after noticing on graphs the existence of a nonlinear pattern with an explosive episode that bursts at its climax. Recently, it has been shown that a linear stationary noncausal process, that is to say an autoregressive process in reverse time, is able to generate features such as bubble patterns. Our interest is to study the behavior of alternative bubble patterns arizing in the mixed causal and noncausal model (MAR) namely a dynamic specification with both leads and lags. It emerges indeed that complex polynomial roots in the MAR model makes the process similar to a process with time varying clustered volatility. We call this patterns seasonal or periodic bubbles. We show that one only needs to detect those roots in either lead or lag polynomial and as such the pseudo-causal representation does not provide additional effect.