On a class of estimation and test for long memory

This paper proposes a new analysis method of the estimation and test for long memory time series. We first introduce the definitions of the time scale series, strong variance scale exponent and weak variance scale exponent, and establish the mathematical equations for the variance scale exponents, with which the time series of the white noise, short memory and long memory can be accurately identified. Two statistics for the hypothesis tests of white noise, short memory and long memory time series are constructed, and the Monte Carlo performance for MSE of the weak variance scale exponent estimator and the empirical size and power of SLmemory statistic is subsequently demonstrated, giving practical recommendations of finite-sample. Finally, brief empirical examples are provided based on Sino-US stock index logarithmic return rate data.