Changes in gene expression programs play a central role in cancer. Chromosomal aberrations such as deletions, duplications and translocations of DNA segments can lead to highly significant positive correlations of gene expression levels of neighboring genes. This should be utilized to improve the analysis of tumor expression profiles. Here, we develop a novel model class of autoregressive higher-order Hidden Markov Models (HMMs) that carefully exploit local data-dependent chromosomal dependencies to improve the identification of differentially expressed genes in tumor. Autoregressive higher-order HMMs overcome generally existing limitations of standard first-order HMMs in the modeling of dependencies between genes in close chromosomal proximity by the simultaneous usage of higher-order state-transitions and autoregressive emissions as novel model features. We apply autoregressive higher-order HMMs to the analysis of breast cancer and glioma gene expression data and perform in-depth model evaluation studies. We find that autoregressive higher-order HMMs clearly improve the identification of overexpressed genes with underlying gene copy number duplications in breast cancer in comparison to mixture models, standard first- and higher-order HMMs, and other related methods. The performance benefit is attributed to the simultaneous usage of higher-order state-transitions in combination with autoregressive emissions. This benefit could not be reached by using each of these two features independently. We also find that autoregressive higher-order HMMs are better able to identify differentially expressed genes in tumors independent of the underlying gene copy number status in comparison to the majority of related methods. This is further supported by the identification of well-known and of previously unreported hotspots of differential expression in glioblastomas demonstrating the efficacy of autoregressive higher-order HMMs for the analysis of individual tumor expression profiles. Moreover, we reveal interesting novel details of systematic alterations of gene expression levels in known cancer signaling pathways distinguishing oligodendrogliomas, astrocytomas and glioblastomas. An implementation is available under www.jstacs.de/index.php/ARHMM.