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Yes, you can. In fact that is the best (only?) way to properly back test a
system. The problem is that Mr. Sornette has not done so. He simply drew
the curve on top of a price chart.
His model was tested You can read under "Predictions"
titled
"Scientific Prediction of Catastrophies: A New
Approach"
http://www.ess.ucla.edu/faculty/sornette/catastrophies.asp#catastrophies
Here is quote:
"In the context of economy, we describe our hypothesis that stock market
crashes are caused by the slow buildup of powerful subterranean forces that
come together in one critical instant. The use of the word ``critical'' is
not purely literary: in mathematical terms, complex dynamic systems such as
the stock market can go through so-called ``critical'' points, defined as the
explosion to infinity of a normally well-behaved quantity. As a matter of
fact, as far as nonlinear dynamic systems go, the existence of critical
points may be the rule rather than the exception. This led us to develop
models and theoretical formulas that have been tested successfully on the
U.S.~stock market crashes of 1929 and 1987: indeed it is possible to identify
clear signatures of near-critical behavior many years before the crashes and
use them to ``predict'' (out of sample) the date where the system will go
critical, which happens to coincide very closely with the realized crash
date. Our theory has also been used to analyze more recent stock market data
leading to a clear signature of an impending critical instability that could
be associated to the turmoil of the US stock market at the end of october
1997. It may come as a surprise that the same theory is applied to epochs so
much different in terms of speed of communications and connectivity as 1929
and 1997. It may be that what our theory addresses is the fundamental
question: has human nature changed?"
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