Low-rate denial of service (LDoS) attacks reduce throughput and degrade quality of service (QoS) of network services by sending out attack packets with relatively low average rate. LDoS attack flows are difficult to detect from normal traffic since it has the property of low average rate. The research on network traffic analysis and modeling shows that network traffic measurement data are irregular nonlinear time series. To characterize and analyze network traffic between attack and non-attack situations, the adaptive normal and abnormal νsupport vector regression (ν-SVR) prediction models are constructed on the basis of the reconstructed phase space. In this paper, the dimension of reconstructed phase space for ν-SVR is optimized by Bayesian information criteria method, and the parameter in the radial basis function is adaptively adjusted by minimizing the within-class distance and maximizing the between-class distance in the feature space. The nonthreshold decision function is obtained through calculating the prediction error of adaptive normal and abnormal ν-SVR prediction models, which is adopted to detect LDoS attacks. Experiments in NS-2 environment show that the adaptive ν-SVR prediction model can effectively predict the network traffic measurement time series, and the probability distribution of time series generated by the adaptive ν-SVR prediction model is quite similar to that of the network traffic measurement data. Experiments also clearly demonstrate the superiority of the proposed approach in LDoS attacks detection.KEYWORDS kernel methods, low-rate denial of service (LDoS), network traffic, nonlinear time series analysis, support vector regression (SVR) of LDoS attacks can be denoted as R × L/T. During LDoS attacking, high intensity pulses are periodically sent to a victim in a specific short interval. The attack duration is short while the time of silence in each period is long, so LDoS attacks attempt to send attack traffic flows at low average rate to elude detection by counter-DoS mechanisms. At present, LDoS detection methods can be divided into frequency domain-based methods and time domain-based methods. 7 In the frequency domain-based methods, He et al 8 proposed a detection system-based wavelet analysis against LDoS attacks, in which the wavelet multiscale analysis was used to extract 5 feature indices of LDoS flows, and back propagation (BP) neural network was used to detect LDoS attacks. Simulation results showed that the detection system-based wavelet analysis can achieve high detection rate (DR) with low computation cost. Wu et al 9 established a spectral energy distribution probability model for detecting LDoS attacks. A probabilistic model was constructed on the basis of LDoS attacks and normal transmission control protocol traffic, and the detection criterion for LDoS attack was calculated by Fourier transform. This approach achieved favorable detection effectiveness, and the DR was obtained by hypothesis test. Zhang et al 10 proposed an adaptive kernel principal component analysi...