Long-context inference enhances the reasoning capability of Large Language Models (LLMs) while incurring significant computational overhead. Token-oriented methods, such as pruning and skipping, have shown promise in reducing inference latency, but still suffer from inherently limited acceleration potential, outdated proxy signals, and redundancy interference, thus yielding suboptimal speed-accuracy trade-offs. To address these challenges, we propose SPTS (Self-Predictive Token Skipping), a training-free framework for efficient long-context LLM inference. Specifically, motivated by the thought of probing the influence of targeted skipping layers, we design two component-specific strategies for selective token skipping: Partial Attention Probing (PAP) for multi-head attention, which selects informative tokens by performing partial forward attention computation, and Low-rank Transformation Probing (LTP) for feed forward network, which constructs a low-rank proxy network to predict token transformations. Furthermore, a Multi-Stage Delayed Pruning (MSDP) strategy reallocates the skipping budget and progressively prunes redundant tokens across layers. Extensive experiments demonstrate the effectiveness of our method, achieving up to 2.46$\times$ and 2.29$\times$ speedups for prefilling and end-to-end generation, respectively, while maintaining state-of-the-art model performance. The source code will be publicly available upon paper acceptance.