In this paper we use a bivariate, fractionally integrated, autoregressive, moving average model of money and real output to extend Fisher and Seater (1993) long-run neutrality requirements to long-memory processes. We derive new restrictions on the order of the nominal and real variable and...

For a process with stationary first differences necessary and sufficient conditions for the variance of the process to be unbounded are given. An example shows that the variance of an integrated process -- while being unbounded -- need not diverge to infinity. Sufficient conditions for the...

In this paper we apply compactly supported wavelets to the ARFIMA(p,d,q) long-memory process to develop an alternative maximum likelihood estimator of the differencing parameter, d, that is invariant to the unknown mean and model specification, and to the level of contamination. We show that...

This paper develops a consistent OLS estimate of a fractionally integrated processes' differencing parameter, using continuous wavelet theory as constructed from smoothing kernels. We show that a log-log linear relationship exists between the variance of the wavelet coefficient and the level at...