We are introducing the new family of the Continuous Time Random Walks (CTRW) with long-term memory within consecutive waiting times. This memory is introduced to the model by the assumption that consecutive waiting times are the analog of CTRW themselves. This way, we obtain the 'Continuous' Time Random Walk in Continuous Time Random Walk. Surprisingly, this type of process, only with the long-term memory within waiting times, can successfully describe slowly decaying nonlinear autocorrelation function of the stock market return. The model achieves this result without any dependence between consecutive price changes. It proves the crucial role of inter-event times in volatility clustering phenomenon.
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