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Unlike previous studies that consider the Chicago Board of Options Exchange (CBOE) implied volatility index (VIX), we examine long memory and fractality in the universe of nine CBOE volatility indices. Using daily data from October 5, 2007, to October 5, 2020, covering calm and crisis periods, we find evidence of long memory and fractality in all indices and a change in the degree of volatility persistence, which points to inefficiency. The long memory of the SKEW index is strong before the onset of three crisis periods, but eases afterwards. The findings provide new insights that matter to investment decisions and trading strategies.