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.
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