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A chaotic semiconductor laser subject to double optical feedback is characterised in terms of the statistical analysis, power spectrum analysis and forecast error analysis of the chaotic dynamics. Varying the relative lengths of the two external cavities, the dynamics are observed and compared to that of a single cavity. We show that in the case of integer multiple external-cavity lengths the round-trip time delays can be deduced from the forecast error analysis. In the case of fractional multiple cavity lengths, only the mean value of the cavity resonance frequencies can be deduced from the power spectra and hence the cavity time delays cannot be found. Cavity time delays that differ more than 0.4 ns can be obtained from the forecast error analysis. In the case of similar cavity lengths, the cavity time delays cannot be extracted. The results show that double optical feedback may offer particular advantages for enhancing security in chaos encryption.