Training Deep Neural Networks for tracking individual cells in biomedical videos requires a large amount of annotated data. The annotation of videos for cell tracking is very time consuming and often requires domain expertise; this explains the limited availability of public annotated data to address important medical problems like tissue repair or cancer treatment. Generating synthetic videos along with their Ground Truth annotations is a promising solution that relies, as a foundational first step, on the synthesis of single cell annotations (or phantoms). Phantoms need to be time consistent, as they have to replicate biological processes that are specific to the cell types. In this work, we propose a novel framework for generating videos of cell phantoms in the Elliptical Fourier Descriptors (EFDs) domain, a compact and geometrically interpretable representation for 2D closed contours. We represent the cell phantom evolution as a multivariate time series of EFD coefficients, introducing a strong prior for cell morphology and enabling the efficient generation of sequences that evolve coherently in time. Our experimental validation proves that modelling the temporal evolution in EFD space enables the generation of biologically plausible phantom videos. Our method can be used in generative pipelines for synthesizing annotated data for cell tracking, thus strongly mitigating the annotation effort for creating new datasets. Our code is available for download here: https://github.com/FrancescoBenedetto99/efd-cell-video-gen.