With novel developments in sequencing technologies, time-sampled data are becoming more available and accessible. Naturally, there have been efforts in parallel to infer population genetic parameters from these data sets. Here, we compare and analyse four recent approaches based on the Wright-Fisher model for inferring selection coefficients (s) given effective population size (N(e)), with simulated temporal data sets. Furthermore, we demonstrate the advantage of a recently proposed approximate Bayesian computation (ABC)-based method that is able to correctly infer genomewide average N(e) from time-serial data, which is then set as a prior for inferring per-site selection coefficients accurately and precisely. We implement this ABC method in a new software and apply it to a classical time-serial data set of the medionigra genotype in the moth Panaxia dominula. We show that a recessive lethal model is the best explanation for the observed variation in allele frequency by implementing an estimator of the dominance ratio (h).