This paper proposes arbitrary reference tier coding (ARTC) schemes to allow the intra directional modes to exploit farther reference tiers for intra prediction. The proposed ARTCs with four reference tiers are applied to a developing future video codec, Joint Exploration Test Model (JEM), under quad-tree (QT) and QT plus binary tree (QTBT) split structures respectively. A joint intra mode and reference tier decision (JMTD) encoding algorithm exclusive to the QTBT is further proposed to efficiently select the intra mode and reference tier. The simulation results show that the ARTC can improve up to 1.2% coding gain compared to the JEM, and the JMTD-based ARTC can reduce 40% encoding time without any coding gain drop compared to the ARTC under QTBT structure. Several analyses are also provided to show that 40-60% encoding time of the ARTC can be further saved with 0.28-0.31% BD-rate increase by disabling some new technologies.