Rocket Science? Forecasting Palestinian Attacks on Israel

• In Event: Conflict Processes and Finance

Abstract

Do conflict processes exhibit repeating patterns over time? And if so, can we exploit the recurring shapes of the time series to forecast the evolution of conflict? Theory has long focused on the sequence of events that precedes conflicts (e.g., escalation or brinkmanship). Yet, current empirical research is unable to represent these complex interactions unfolding over time. This is because it attempts to match cases on the value of covariates, and not on their structure or shape. In other words, it cannot easily represent real-world relations which may, for example follow a long alternation of escalation and détente, in various orders and at various speeds, before finally breaking down into conflict. Lags of a few order might be included in a regression to account for issues of autocorrelation, but they cannot represent the potentially complex trajectories that pre-conflict events take. In short, correlation (and its various regression-based derivatives), is a poor metric for complex nonlinear patterns that may additionally be stretched or shifted.
Here, we instead study here escalation patterns using recent machine-learning methods derived from information geometry, clustering, and pattern recognition in time series, including geometric-based approaches. Our goal is to supplement typical approaches with clustering and prototyping methods to extract shapes and ideally better understand the patterns of escalation into war.

We apply these methods to a particularly challenging task: forecasting the precise timing of Palestinian rocket and mortar attacks on Israel. Using four years of minute-level prices for 500 Israeli stocks, we find that financial asset prices react on average 30 minutes ahead of the launch of a rocket. To obtain this result, we relied on various distance measures for time series (shape-based such as Dynamic Time Warping, feature-based such as Wavelet decomposition, etc.). The distance from one time series to another is calculated for every two-hour period, every stock, and every method, and these distances are then aggregated in an Ensemble model, resulting in a forecasted probability of a rocket attack. The early warning signals that we uncover are both more accurate (esp. fewer false negatives), and provide earlier warnings than existing approaches. These results have practical uses, as Israel’s Home Front Command only gives its citizen less than a minute to seek cover. Our forecast can significantly extend this early warning time.

Finally, we validate our result in a true out-of-sample manner. Using live market data and minute-level rocket attack data from Israel’s home front command, we publicly broadcast our forecasts in real time for every minute of every day and will continue to do so until the conference, when we will report our results.

Author

• Thomas Chadefaux, Trinity College Dublin