The Effects of Systematic Sampling and Temporal Aggregation on Discrete Time Long Memory Processes and Their Finite Sample Properties

This study investigates the effects of varying sampling intervals on the long memory characteristics of certain stochastic processes. We find that although different sampling intervals do not affect the decay rate of discrete time long memory autocorrelation functions in large lags, the autocorrelation functions in short lags are affected significantly. The level of the autocorrelation functions moves upward for temporally aggregated processes and downward for systematically sampled processes, and these effects result in a bias in the long memory parameter. For the ARFIMA(0,d,0) process, the absolute magnitude of the long memory parameter, |d|, of the temporally aggregated process is greater than the |d| of the true process, which is greater than the |d| of the systematically sampled process. We also find that the true long memory parameter can be obtained if we use a decay rate that is not affected by different sampling intervals.