Adaptive Non-Markov Memory with Threshold Observers: A Unified Architecture for Event Forecasting

It is well known that many sequential events follow cycles, can cluster after earlier scattered events, resume after long pauses or change distribution when the underlying system changes state. Most forecasting methods, however, restrict how the past is used, by weighting only recent observations and assuming a fixed decay rate of memory or fitting a dependence modelthat is then held fixed. This paper further develops the adaptive non-Markov memory (ANM) model introduced in an earlier paper [1], which keeps the complete observed history and searches it at multiple timescales for cycles, takes into account delayed recurrences, regime changes and similar past states. This updated model also introduces a threshold observer layer,which forecasts whether or not a measured quantity will cross a given threshold. After every time step, whether an event occurs or not, it also updates the weight given to each form of historical evidence (refer Table 2). ANM was tested on a wide variety of datasets, synthetic event processes, simulated control systems and 22 real datasets (45 series or recordings). Before most tests, the datasets, comparators and pass criteria were recorded and the code was frozen by its SHA-256 hash; the two exceptions are identified and every criterion is reported, including those not met. Against renewal, ETAS and Markov models, ANM captured 93–95% of the achievable gain on strongly cyclic processes and was never significantly less accurate on real data. On five real series with strong cycles or persistence it reduced log-loss by 23–97%. Against GARCH and neural Hawkes-type models, of 47 real-data comparisons, 27 showed no significant difference, 18 significantly favoured ANM and 2 favoured the comparator. Against gradient boosting type models [2] and ARIMA [3] the results were mixed. Of the 15 main real dataset series, ANM was not significantly different from the best of them on 11, significantly more accurate on 3 and significantly less accurate on 1. On the chaotic Santa Fe laser recordings [4, 5], it forecast readings above the fitting-period 90th percentile more accurately than alleight other models tested (53–98% lower log-loss). Gradient boosting was more accurate on calendar-driven US daily births [6, 7] when given calendar features and on a chaotic transistor circuit [8] and friction measurements tests [9]. On the circuit test the LSTM-based comparator [10] was also more accurate. ANM was more accurate than gradient boosting on rotatingconvection [11] and double pendulum [12] tests. Results on real chaotic systems are therefore mixed and a general advantage remains unconfirmed pending further trials. We conclude that past observations improve forecasts when a process repeatedly leaves identifiable patterns in its history, at timescales that need not be fixed in advance. Retaining more history does notadd predictability when the process contains little recoverable structure.