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Annals of Statistics
Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter $(\gamma)$, at the frequency of principal interest, zero; for short-memory series $\gamma=0$ automatically. The latter case has also been stressed under long memory, along with the "fractional differencing" case $\gamma=(\delta_2-\delta_1)\pi /2$, where $\delta_1$, $\delta_2$ are the memory parameters of the two series. We develop time domain conditions under which these are and are notdoi:10.1214/07-aos545 fatcat:pm6egarjqrhxxj2dbbapo7gcbq