Intraday downward/upward multifractality and long memory in Bitcoin and Ethereum markets: An asymmetric multifractal detrended fluctuation analysis

•Long memory and weak-form efficiency of cryptocurrency market are examined.•High-frequency data of two major cryptocurrencies, Bitcoin and Ethereum, are used.•Asymmetric multifractal detrended fluctuation analysis method is applied.•Structural breaks, long memory, and asymmetric multifractality are in both markets.•The Bitcoin market is more inefficient for overall, upward, and downward trends.