We study how quantization, occurring when a continuously varying process is approximated by or observed on a grid of discrete values, changes the properties of a Gaussian long-memory process. By computing the asymptotic behavior of the autocovariance and of the spectral density, we find that the quantized process has the same Hurst exponent of the original process. We show that the log-periodogram regression and the Detrended Fluctuation Analysis (DFA) are severely negatively biased estimators of the Hurst exponent for quantized processes. We compute the asymptotics of the DFA for a generic long-memory process and we study them for quantized processes.
↧
