A Time Series Analysis of International Piracy

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Piracy is defined as any illegal act of violence, detention, or any act of depredation committed for private ends against a ship on the high seas or otherwise outside of the jurisdiction of a state. Incidents of armed robbery against ships, similar acts which happen while a ship is within the territorial waters of a state, have also been included.

Figure 1 provides the time series plot on the monthly number of incidents of international piracy, from 1995 to the present. Whereas the 1995-1997 period appeared to have maintained an overall level of approximately 20 incidents per month, the subsequent peiord seems less uniform. How much of this is attributable to seasonality? How much is due to a shift in the underlying trend? The next graph separates the seasonal component from the data.

Figure 1 - International Piracy

Figure 2 - Monthly Seasonal Variation

Figure 2 provides a plot of the monthly seasonal variation, calculated over the period of January 1995 through March 2002, for the number of international piracy incidents. The month of January experiences the highest number of incidents on average, and February experiences the lowest number on average. The remaining months vary slightly from the average, but only January and February showed significant seasonal variations (at alpha=0.05).

The next set of analyses study changes in the data, once seasonality has been removed as a source of variation. The search can now be conducted to find unexpected changes in the underlying trend; the results of this analysis are provided in Figure 3.

Figure 3 - International Piracy With Interventions

Statistical process control (SPC) procedures were applied to the model to search for additional shifts in the data. March 2000, indicated by the red point on the graph, indicates when a significant one-period drop occurred; the effect of this decrease was only experienced for that one month. The green points on the curve highlight changes in the data that resulted in longer-term changes in the underlying level. Overall, there is no continuous long-term upward slope to this set of data from 1995 through 2001, but there were three periods of significant upward drift around January 1999, November 1999 and September 2000. A significant downward drift was signaled on March 2001. These changes in 2000 were driven primarily by an increase in incidents in the Indian Ocean and the Malacca Straits. We would expect to see changes in the underlying trends around these periods of significant change.

Figure 4 provides the final underlying trend to the data. As suggested by preliminary visual analysis, the general level number of incidents from 1996 through 1998 was steady, followed by a significant rise in the 1999 and early 2000. But this rise was followed by a significant fall in the number of incidents in 2001. What remains to be seen is whether the recent decline eventually levels off to the previously experienced number of incidents in the mid-1990's.

Figure 4 - International Piracy with Underlying Trend