Genomic DNA copy number alterations are characteristic of many human diseases including cancer. Various techniques and platforms have been proposed to allow researchers to partition the whole genome into segments where copy numbers change between contiguous segments, and subsequently to quantify DNA copy number alterations. In this paper, we incorporate the spatial dependence of DNA copy number data into a regression model and formalize the detection of DNA copy number alterations as a penalized least squares regression problem. In addition, we use a stationary bootstrap approach to estimate the statistical significance and false discovery rate.