Executive’s summary

Do Major Marine Accidents occur randomly?Alexandros M. Goulielmos (*), former Professor of Marine Economics & MrsNikiGatzoli (**), Research and Teaching assistant, (*) (**) Dept. of Maritime Studies, University of Piraeus

Executive’s summary • A great number of ships =1788 involved in major marine accidents between 2004-2008. • The papertried to resolve the paradox: why in certain, (only 3), geographical areas major marine accidents reach 70% of the total? • The generalized (by Hurst) Einstein’s formula for a random time series covering distance at the square root of time is used.

Hurst exponent from ‘Rescaled Range Analysis’, (+ MATLAB 2009 and NLTSA 2000), found equal to 0.50, as it should (=Random Walk). This refers to the 1788 major marine accidents recorded weekly by Lloyd’s, for 2004-2008, in dwt. • Next we tested the 1070 from the 1788 (60%) major marine accidents that we managed to allocate their dwt in the 12 geographical areas for the same period. • Hurst exponent found equal to 0.43<0.50 (speed< random). This means that data per geographical area are not random (but anti-persistent). This is Pink noise-turbulence.

Ships damaged by a major accident were 27.55 m dwt allocated: 31% in ‘N. Sea and the Baltic’, 20% in ‘Mediterranean and Black Sea’ and 19% in ‘China Sea’=70%). • These research findings challenge all those who believe that major marine accidents are due to bad luck and thus nothing can be done. IN MORE DETAIL

‘Hurst exponent’ measures Brownian motion (=‘Random Walk’). The previous change in the value of a variable (e.g. major marine accidents) is not correlated in long term to its future or past changes. • “Hurst coefficient” is given by: R/S=c* [1], where R= range and S= standard deviation. [1] is a general form of Einstein’s (1905) equation D=√T [2], if: R/S =R (the distance covered), T=n (time index/no of observations), H=√ and c= a constant. H ranges between 0 and 1. • In [2], time series is independent for increasing values of n, assumed to have a zero mean and variance equal to 1. Equation [1] applies into time series that are not independent, but have long term dependence.

‘Rescaled Range Analysis’ determines long-memory effects and ‘fractional’Brownian motion. • If the speed of time series ≠ the square root of time, is not random. This was our criterion of the random pattern in major marine accidents.

Figure 1 below is made up by the dwts of the 1788 major cases of marine accidents of 12 kinds occurred on all sizes of ships, between 2004 and 2008. • Certain large ships are involved of some 190,000 dwt, though the bulk of marine accidents involve ships below 80,000 dwt and certainly below 40,000.

Figure 1: Major cases of Marine accidents (1788) of ships worldwide, 2004-2008, in dwt per case. DWTS. Number of major accidents in dwt. Source: Lloyd’s and Miss V. Vlysidou.

Using ‘Nonlinear time series analysis program’ (2000), we found H 0.50 (0.502024) for n≥10 estimated by regression using first logarithmic differences as a filter (Figure 2). H=0.50 for randomness. • Moreover, if data are random then R/S is in linear relationship with √n, where R is the range of time series, S, the standard deviation, and n the number of observations. • If we divide R/S by √n we obtain a measure of the probability that data has long-term dependence. This gave a probability < 0.005~0 to be long-term dependent.

Figure 2: H exponent of 1693-1 major cases of marine accidents by dwt, 2004-2008. Source: As in figure 2, using MATLAB 7.9.0 (2009b).

Data transformedthe 1788 major marine accidents were allocated per geographical area where each accident took place. The no of accidents fell to 1070 either because the area was missing or the dwt was not known. • Applying NLTSA (2000) computer program, we found H exponent equal to 0.43 (0.433457) for n≥10. Time series are anti-persistent (‘pink noise’). Time series reverses itself more oftenthan random. • Blue line in Figure 3 does not coincide with red line. The red line is Einstein’s benchmark for a speed at the square root (0.50) of time for randomness in logs.

Figure 3: 1070 Major marine accidents 2004-2008 occurred at a slower speed than random when tested in their geographical area.

Figure 4: Hurst exponent for the 1070 major marine accidents per geographical area and dwt, 2004-2008. Source: MATLAB 7.9 and data based on Lloyd’s.

Table 1 shows how the 27.5 million dwt involved in major marine accidents 2004-2008 are allocated per geographical area where the accident took place. • It is clear that only 3 areas (!) monopolize major marine accidents: North Sea and Baltic; Mediterranean and Black Sea and Sea of China (=70.06%).

Table 1: Major marine accidents per area, dwt and %, 2004-2008 Source: Our calculations from data base.

This phenomenon of the heavy concentration of major marine accidents in only 3 geographical areas is also shown in Figure 5. DWTs damaged above. Source: as perprevious Figure. Areas in X axis. As shown, areas 6, 7 and 11 dominate, out of 12.

Major marine accidents are turbulent with one possible reason theenvironment in which ships work. • Turbulence has two traits: (1) scaling and (2) long-term dependence. Many natural and economic phenomena are turbulent: areas & reserves of oil fields, valuation of gold; uranium & diamond mines, as well as storms and earthquakes. • Also: weather, affecting harvests and harvests affecting prices; the distribution of natural resources like oil, gold etc. affecting supply and prices. • The size of firms also follows a scaling pattern and thus concentration affects profit, and stock prices.

Turbulence is found all round us. Every event with no matter how remote or long ago, echoes across all other events. Turbulence is fundamentally a new way of analyzing marine accidents (our suggestion). • Marine accidents are dynamic, unpredictable and often dangerous systems for transferring ‘wealth’ (cargo) on multi-million means = vessels. • These systems are as important to understand as the wind, the rain and the flood.

CONCLUSIONS • We proved that when major marine accidents are tested over the time they have occurred are random in Einstein’s sense. • When we examined major marine accidents in the geographical areathey have occurred, then they were found anti-persistent, travelling with a speed at 0.43 of the square root of time. • H signifies anti-persistence as it characterizes a system covering less distance than a random one. For this to be so it must reverse itself more frequently than a random process.

Major marine accidents are turbulent systems described by stable Levy distributions with infinite mean and variance. Volatility is unstable. A rise in major marine accidents is not followed by an equivalent decrease. • Antipersistenceis not unique in shipping, but par excellence is met in the volatility of stock market prices. • Volatility = risk. So, shipping is a risky business also bythe occurrence of major marine accidents, where in just 5 years more than 27.5 million dwt of ships were accidentally damaged. • THANK YOU FOR YOUR PATIENCE

Executive’s summary