A. Shapoval 1,2 , V. Gisin 1 , V . Popov 1,3,4. 1. Finance academy under the government of the RF. 2. International institute of earthquake prediction thoory. 3. Moscow State University. 4. Space research institute. Super-exponential trends as the precursors of crashes.
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A. Shapoval1,2, V. Gisin1, V. Popov1,3,4
1. Finance academy under the government of the RF
2. International institute of earthquake prediction thoory
3. Moscow State University
4. Space research institute
Super-exponential trends as the precursors of crashes
Are crises predictable?
Scheme of actions:
1. To detect the indicators of crises.
2. To construct the prediction algorithms involving these indicators.
Hypothesis. Super-exponential growth (speculative bubbles) preceeds the crashes
m>1, w(t) – the Wiener process, dj = 0 or 1
Due to he special arrangements of the terms there exists the filter mapping the data into the normal sample!
It gives a criterion of the model adequacy
The solution is derived analytically!
Gel'fand, Guberman, Keilis-Borok, Knopoff, Press, Ranzman, Rotwain Sadovsky (1976)
Prediction algorithm of any nature divides the time axisinto the intervals of two sorts:(1) the alarm is announced (the event-to-predict is expected);(2) the alarm is not announced.
t the collection of the sliding windows
[t, t-wi), iI
di– the deviation of the solution from the data on [t, t-wi),
A(t) = #(di(t) < d*)
A(t) > A* bubbles
bA,N (t) – the trend of А on [t, t-N)
bX,N (t) – the trend ofX on [t, t-N)
Either bA,N (t)<0, or bX,N (t)<0
the bubbles the alarm
A(t) > A*
A «calm period»
Crash occurred or alarm was declared T days ago