Replicate the simulation study whose results are summarized in Tables 411a and 411b, which concern the variances of various estimators of the power-law exponent α associated with four different...

Replicate the simulation study whose results are summarized in Tables 411a and 411b, which concern the variances of various estimators of the power-law exponent α associated with four different fractionally differenced (FD) processes. These tables make use of the sample variances of estimators of α based on 10,000 independent realizations of each FD process. In addition to variances, investigate the sample biases, squared biases and MSEs. To replicate this study, you need to generate simulated FD time series, which can be done using the circulant embedding method (Craigmile, 2003). This method is described in Section 11.2 and requires knowledge of the ACVS for an FD process, which can be computed recursively once the variance s0 is known:

The ACVS involves the same two parameters
  and δ as does the FD SDF stated in Equation (407). The power-law exponent α and δ are related by α = −2δ. The statistical properties of the estimators of α do not depend on how
  is set; hence, for the simulation study, it suffices to just set s₀
= 1.