Rare Events Forecasting Using a Residual-Feedback GMDH Neural Network

The prediction of rare events is a pressing scientific problem. Events such as extreme meteorological conditions, may aggravate human morbidity and mortality. Yet, their prediction is inherently difficult as, by definition, these events are characterised by low occurrence, high sampling variation, and uncertainty. For example, earthquakes have a high magnitude variation and are irregular. In the past, many attempts have been made to predict rare events using linear time series forecasting algorithms, but these algorithms have failed to capture the surprise events. This study proposes a novel strategy that extends existing GMDH or polynomial neural network techniques. The new strategy, called residual-feedback, retains and reuses past prediction errors as part of the multivariate sample data that provides relevant multivariate inputs to the GMDH or polynomial neural networks. This is important because the strength of GMDH, like any neural network, is in predicting outcomes from multivariate data, and it is very noise-tolerant. GMDH is a well-known ensemble type of prediction method that is capable of modelling highly non-linear relations. It achieves optimal accuracy by testing all possible structures of polynomial forecasting models. The performance results of the GMDH alone, and the extended GMDH with residual-feedback are compared for two case studies, namely global earthquake prediction and precipitation forecast by ground ozone information. The results show that GMDH with residual-feedback always yields the lowest error.

1. Introduction

Accurate prediction of rare high-impact events is a difficult yet popular research problem. The difficulty is due to the large sampling uncertainty caused by the infrequent occurrence of the events, and the popularity is due to the potential mitigation of disasters if the problem is solved. In the past decades, the most popular type of forecasting technique has been based on the regression of a future prediction based on past samples. This forecast technique is inherited from the concept of time series decomposition, in which a time series is believed to be modelled individually according to four components: trend, seasonality, cycle, and white noise. Since the 1970s, many such techniques have become prevalent, including AR, MA, ARIMA, SARIMA, ARIMAX, etc. In this study, these techniques are generally referred to as linear forecasting techniques (LFT). Although all of these techniques produce satisfactory forecasting results for forecasting the mean and acceptable levels of variance, they have several limitations. First, because these algorithms are based on estimating the moving average values over a time series, the forecast is usually in the form of a mean value. In some special cases, such as predicting disasters, the rare events rather than the average values or normal happenings are of interest. In this study, we are concerned with the extraordinary cases that are rare even in large historical datasets. The second shortcoming is the problem of choosing the optimal parameters for calibrating LFTs. A casual choice of these parameters will lead to an extremely poor fit of the forecast model to the actual data. Third, LFTs may work very well for a time series that exhibits strong seasonality and/or long-term trends. However, for other time series, they may result in over- or under-forecasting, especially if the white noise component dominates the characteristics of the time series. The forecasting model easily becomes unstable when the time series exhibits a large extent of randomness and fluctuation, the “average-oriented” forecasting model fails badly to predict the peak values.