Bivariate time series models are considered that are suitable for estimation, that have interpretable parameters and that can capture the general semi-parametric formulation of bivariate long-range dependence, including a general phase. The models also allow for short-range dependence and fractional cointegration. A simulation study to test the performance of a conditional maximum likelihood estimation method is carried out, under the proposed models. Finally, an application is presented to the U.S. inflation rates in goods and services where models not allowing for general phase suffer from misspecification. 1 The following convention is used here. The autocovariance function is defined as (n) = X n X ′ 0 and the spectral density f ( ) satisfies (n) = ∫ − e in f ( )d . The convention is different from Kechagias and Pipiras (2015), where X 0 X ′ n is used as the autocovariance function, but is the same as in Brockwell and Davis (2009) and Pipiras and Taqqu (2017). We conclude this section by arguing that the model (1.6) and (1.7) can also be used to capture general phase when one of the component series is SRD (with the corresponding d = 0) and the other is LRD. (The component series can also be both SRD but this case is not particularly interesting since for two SRD series, their spectral density at zero is the sum of autocovariances at all lags and hence has zero phase = 0.) We formulate this as The one-sided FIVARMA(p, D, q) series (with c = 0 in (3.10)) have been more popular in the literature, with Lobato (1997), Sela and Hurvich (2009) and Tsay (2010) being notable exceptions. In particular, Sela and Hurvich 3 The names VARFIMA and FIVARMA refer to the facts that the fractional integration (FI) operator Δ c (B) −1 is applied to the MA part in (3.9) and after writing X n = Δ c (B) −1 Φ(B) −1 Θ(B)Z n , it is applied to the VARMA series in (3.10).wileyonlinelibrary.com/journal/jtsa Since (Y n+h−s |Y 1 , … , Y N ) =Ŷ n+h−s|n , the relation (4.17) yields (4.12).Next, we subtract (4.12) from (4.16) to get