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On Thursday, March 11 2004, during the morning traffic of people going
to work in Madrid, several bombs
were exploded in commuter trains as they pulled
into stations. These terrorist attacks were highly coordinated, with the
first at 07:39, local time, followed closely by three more nearby. A few
minutes later at 07:45 and 07:55, two more. About 200 people were
killed and some 1500 were injured. At 10:10 two more bombs
were found by police and detonated by bomb squads. Examination of the
un-detonated bombs revealed that they were designed to explode when a
mobile phone in the package was called.
I was traveling in Brazil, but the local papers had detailed reports on
the attacks. I was able to establish
the parameters of the formal prediction for
later analysis. Two other people, Per Lassen and Dick Bierman, also
suggested the Madrid bombings and the anti-terrorist
demonstrations the next day (12 March) should be examined; they are
included as predictors in the results table.
Following precedents from other terrorist attacks,
I set the period from 07:00 to 12:00 as the formal
prediction (6 to 11 GMT), to include some time before the first
explosion and several hours of the aftermath. The trend over this period
is extreme -- but it is a negative slope, opposite to the standard
prediction. The Chisquare is 17634 on 18000 df, with corresponding
p-value of 0.974. The first of the two following figures shows the
formal analysis.
An exploratory examination of the context is shown in
the second figure, which plots the data for the whole GMT day. It is
apparent that the random walk changed at about the time of the terrorist
attacks, and continued in an extremely unlikely negative trend for about
10 hours. While it is not appropriate to calculate probabilities for
this selected segment, it is in the extreme tail of the distribution of
such analyses performed for all days in the 5.5 year database.
The long-continuing trend is reminiscent of the two-day persistence of
deviation following the Sept 11 2001 terrorist attacks in the US.
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