Coronary artery diseases (CADs) are the leading cause of death worldwide and early diagnosis is crucial for timely treatment. To address this, our study presents a novel automated Artificial Intelligence (AI)-based Hybrid Anomaly Detection (AIHAD) technique that combines various signal processing, feature extraction, supervised, and unsupervised machine learning methods. By jointly and simultaneously analyzing 12-lead cardiac sympathetic nerve activity (CSNA) and electrocardiogram (ECG) data, the automated AIHAD technique performs fast, early, and accurate diagnosis of CADs. In order to develop and evaluate the proposed automated AIHAD technique, we utilized the fully labeled STAFF III and PTBD databases, which contain the 12-lead wideband raw recordings non-invasively acquired from 260 subjects. Using these wideband raw recordings, we developed a signal processing technique that simultaneously detects the 12-lead CSNA and ECG signals of all subjects. Using the pre-processed 12-lead CSNA and ECG signals, we developed a time-domain feature extraction technique that extracts the statistical CSNA and ECG features critical for the reliable diagnosis of CADs. Using the extracted discriminative features, we developed a supervised classification technique based on Artificial Neural Networks (ANNs) that simultaneously detects anomalies in the 12-lead CSNA and ECG data. Furthermore, we developed an unsupervised clustering technique based on Gaussian mixture models (GMMs) and Neyman-Pearson criterion, which robustly detects outliers corresponding to CADs. Using the automated AIHAD technique, we have, for the first time, demonstrated a significant association between the increase in CSNA signals and anomalies in ECG signals during CADs. The AIHAD technique achieved highly reliable detection of CADs with a sensitivity of 98.48 %, specificity of 97.73 %, accuracy of 98.11 %, positive predictive value of 97.74 %, negative predictive value of 98.47 %, and F1-score of 98.11 %. Hence, the automated AIHAD technique demonstrates superior performance compared to the gold standard diagnostic test ECG in the diagnosis of CADs. Additionally, it outperforms other techniques developed in this study that separately utilize either only CSNA data or only ECG data. Therefore, it significantly increases the detection performance of CADs by taking advantage of the diversity in different data types and leveraging their strengths. Furthermore, its performance is comparatively better than that of most previously proposed machine and deep learning methods that exclusively used ECG data to diagnose or classify CADs. Additionally, it has a very low implementation time, which is highly desirable for real-time detection of CADs. The proposed automated AIHAD technique may serve as an efficient decision-support system to increase physicians' success in fast, early, and accurate diagnosis of CADs. It may be highly beneficial and valuable, particularly for asymptomatic patients, for whom the diagnostic information provided by ECG alone is not sufficient to reliably diagnose the disease. Hence, it may significantly improve patient outcomes by enabling timely treatments and considerably reducing the mortality of cardiovascular diseases (CVDs).