When modelling the stable baseline component of a riometer voltage series, the degradation of statistical performance can be significant if either the data are noisy or the underlying stochastic process is highly nonstationary. It is desirable to explore models which balance the high degree of stability of a quiet-day curve with low computation time. This paper introduces a multitaper method for generating quiet-day curves. A novel metric is introduced for determining the overlap fraction in a section-overlap model of the stable baseline component. The paper is also important because of its introduction of competitive methods for reconstructing periodic elements in an arbitrary random voltage signal.