In recent years, scale, frequency and complexity of cyber-attacks have been continuously on the rise. As a result, it has significantly impacted our daily lives and society as a whole. Never before have we had such an urgent need to defend against cyber-attacks. Previous studies suggest that it is possible to detect rootkits and control-flow attacks with high accuracy using information collected from hardware level. For data-only exploits, however, where the control-flow of the victim application is strictly conserved while its behavior may only be slightly modified, high accuracy detection is much more difficult to achieve. In this study, we propose the use of low-level hardware information collected as a short time series for the detection of data-only malware attacks. We employed several representative classification algorithms, e.g., linear regression (LR), autoencoder (AE), stacked denoising autoencoder (SDA), and echo state network (ESN). We build one-class classifiers that either use individual samples collected via monitoring hardware-level events or use multiple samples of hardware events collected at different time during execution, but all with only the knowledge from regular behavior. Using several real-life attacks as case studies, we examined their detection accuracy when confronted with malicious behavior. Our experimental results show that our SDA- and ESN-based approaches can achieve an average detection accuracy of 97.75% and 98.36% for the exploits studied, respectively. Our study suggests that when the hardware events are monitored at different time spots during the execution of the vulnerable application, our SDA- and ESN-based approaches have the potential to boost the detection accuracy for data exploits.