Genomic samples collected from a single population over several generations provide direct access to the genetic diversity changes occurring within a specific time period. This provides information about both demographic and adaptive processes acting on the population during that period. A common approach to analyze such data is to model observed allele counts infinite samples using a Hidden Markov Model (HMM) where hidden states are true allele frequencies over time (i.e. a trajectory). The HMM framework allows to compute the full likelihood of the data, while accounting both for the stochastic evolution of population allele frequencies along time and for the noise arising from sampling a limited number of individuals at possibly spread out generations. Several such HMM methods have been proposed so far, differing mainly in the way they model the transition probabilities of the Markov chain. Following Paris et al. (2019a), we consider here the Beta with Spikes approximation, which avoids the computational issues associated to the Wright-Fisher model while still including fixation probabilities, in contrast to other standard approximations of this model like the Gaussian or Beta distributions. To facilitate the analysis and exploitation of genomic time series data, we present an improved version of Paris et al. (2019a) s approach, denoted SelNeTime, whose computation time is drastically reduced and which accurately estimates effective population size (assuming no selection) or the selection intensity at each locus (given a previously estimated value of N). This method is implemented in a user friendly python package, which also allows to easily simulate genomic time series data under a user-defined evolutionary model and sampling design.