This paper presents a novel approach for trajectory anomaly detection using an autoregressive causal-attention model, termed LM-TAD. This method leverages the similarities between language statements and trajectories, both of which consist of ordered elements requiring coherence through external rules and contextual variations. By treating trajectories as sequences of tokens, our model learns the probability distributions over trajectories, enabling the identification of anomalous locations with high precision. We incorporate user-specific tokens to account for individual behavior patterns, enhancing anomaly detection tailored to user context. Our experiments demonstrate the effectiveness of LM-TAD on both synthetic and real-world datasets. In particular, the model outperforms existing methods on the Pattern of Life (PoL) dataset by detecting user-contextual anomalies and achieves competitive results on the Porto taxi dataset, highlighting its adaptability and robustness. Additionally, we introduce the use of perplexity and surprisal rate metrics for detecting outliers and pinpointing specific anomalous locations within trajectories. The LM-TAD framework supports various trajectory representations, including GPS coordinates, staypoints, and activity types, proving its versatility in handling diverse trajectory data. Moreover, our approach is well-suited for online trajectory anomaly detection, significantly reducing computational latency by caching key-value states of the attention mechanism, thereby avoiding repeated computations.