The phrase "deterministic trend" refers to a consistent and predictable pattern or direction in a set of data. It means that the data is following a specific trend that can be determined or forecasted. Full definition
Cointegration indicates that internal climate variability and / or the omission of some components of radiative forcing (e.g., stratospheric water vapor, black or organic carbon, nitrite aerosols, etc.) do not impart a stochastic or deterministic trend that would interfere with the interpretation of temperature changes at the subdecadal scale (SI Appendix). (pnas.org)
This representation is flawed both statistically, because time series that contain a stochastic trend can not be approximated by a deterministic trend (13), and historically, because the time trend overstates gains in radiative forcing during the 1950's and overstates gains during the last 10 y (Fig. 1). (pnas.org)
Zheng and Basher (1999) use similar time - series models and show that deterministic trends are detectable over a large part of the globe. (ipcc.ch)