Cough is a common symptom of numerous respiratory diseases. In certain cases, such as asthma and COPD, early identification of coughs is useful for the management of these diseases. This paper presents an algorithm for automatic identification of cough events from acoustic signals. The algorithm is based on only four features of the acoustic signals including LPC coefficient, tonality index, spectral flatness and spectral centroid with a logistic regression model to label sound segments into cough and non-cough events. The algorithm achieves sensitivity of of 86.78%, specificity of 99.42%, and F1-score of 88.74%. Its high performance despite its small size of feature-space demonstrate its potential for use in remote patient monitoring systems for automatic cough detection using acoustic signals.