Approximating long-memory processes with low-order autoregressions: Implications for modeling realized volatility

Several articles have attempted to approximate long-memory, fractionally integrated time series by fitting a low-order autoregressive AR(p) model and making subsequent inference. We show that for realistic ranges of the long-memory parameter, the OLS estimates of an AR(p) model will have non-standard rates of convergence to non-standard distributions. This gives rise to very poorly estimated AR parameters and impulse response functions. We consider the implications of this in some AR type models used to represent realized volatility (RV) in financial markets.