Time series with bubble-like patterns display an unbalance between growth and acceleration, in the sense that growth in the upswing is “too fast” and then there is a collapse. In fact, such time series show periods where both the first differences (1-L) and the second differences (1-L)2 of the data are positive-valued, after which period there is a collapse. For a time series without such bubbles, it can be shown that 1-L2 differenced data should be stable. A simple test based on one-step-ahead forecast errors can now be used to timely monitor whether a series experiences a bubble and also whether a collapse is near. Illustration on simulated data and on two housing prices and the Nikkei index illustrates the practical relevance of the new diagnostic. Monte Carlo simulations indicate that the empirical power of the test is high.

acceleration, growth, speculative bubbles, test
Time-Series Models; Dynamic Quantile Regressions (jel C22)
Erasmus School of Economics
hdl.handle.net/1765/39598
Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus School of Economics

Franses, Ph.H.B.F. (2013). Are we in a bubble? A simple time-series-based diagnostic (No. EI 2013-12). Report / Econometric Institute, Erasmus University Rotterdam (pp. 1–27). Erasmus School of Economics. Retrieved from http://hdl.handle.net/1765/39598