We present a new method to detect and adjust for noise and artifacts in functional MRI time series data. We note that the assumption of stationary variance, which is central to the theoretical treatment of fMRI time series data, is often violated in practice. Sporadic events such as eye, mouth, or arm movements can increase noise in a spatially global pattern throughout an image, leading to a non-stationary noise process. We derive a restricted maximum likelihood (ReML) algorithm that estimates the variance of the noise for each image in the time series. These variance parameters are then used to obtain a weighted least squares estimate of the regression parameters of a linear model. We apply this approach to a typical fMRI experiment with a block design and show that the noise estimates strongly vary across different images and that our method detects and appropriately weights images that are affected by artifacts. Furthermore, we show that the noise process has a global spatial distribution and that the variance increase is multiplicative rather than additive. The new algorithm results in significantly increased sensitivity in the ability to detect regions of activation. The new method may be particularly useful for studies that involve special populations (e.g., children or elderly) where sporadic, artifact-generating events are more likely.