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Classical time series models have failed to properly assess the risks that are associated with large adverse stock price behaviour. This article contributes to autoregressive moving average model-GARCH (ARMA-GARCH) models with standard infinitely divisible innovations and assesses the performance of these models by comparing them with other time series models that have normal innovation. We discuss the limitations of value at risk (VaR) and aim to develop early warning signal models using average value at risk (AVaRs) based on the ARMA-GARCH model with standard infinitely divisible innovations. Empirical results for the daily Dow Jones Industrial Average Index, the England Financial Times Stock Exchange 100 Index and the Japan Nikkei 225 Index reveal that estimating AVaRs for the ARMA-GARCH model with standard infinitely divisible innovations offers an improvement over prevailing models for evaluating stock market risk exposure during periods of distress in financial markets and provides a suitable early warning signal in both extreme events and highly volatile markets.