Owing to the quick development of high-throughput techniques and the generation of various "omics" datasets, it creates a prospect of performing the study of genome-wide genetic regulatory networks. Here, we present a sophisticated modelling framework together with the corresponding inference methods for accurately estimating genetic regulation from time-series microarray data. By applying our non-linear model on human p53 microarray expression data, we successfully estimated the activities of transcription factor (TF) p53 as well as identified the activation/inhibition status of p53 to its target genes. The predicted top 317 putative p53 target genes were supported by DNA sequence analysis. Our quantitative model can not only be used to infer the regulatory relationship between TF and its downstream genes but also be applied to estimate the protein activities of TF from the expression levels of its target genes.