Long memory models for daily and high frequency commodity futures returns

The volatility of daily futures returns for six important commodities are found to be well described as FIGARCH, fractionally integrated processes, whereas the mean returns exhibit very small departures from the martingale difference property. Several years of high frequency intraday commodity futures returns are also found to have very similar long memory in volatility features as the daily returns. Semiparametric local Whittle estimation of the long memory parameter in absolute returns also finds very significant long memory features. Estimating the long memory parameter across many different data sampling frequencies provides consistent estimates of the long memory parameter, suggesting that the series are self‐similar. The results have important implications for empirical work using commodity futures price data.