Acute and chronic insomnia have different causes and may require different treatments. They are investigated with multi-night nocturnal actigraphy data from two sleep studies. Two different wrist-worn actigraphy devices were used to measure physical activities. This required data pre-processing and transformations to smooth the differences between devices. Statistical, power spectrum, fractal and entropy analyses were used to derive features from the actigraphy data. Sleep parameters were also extracted from the signals. The features were then submitted to four machine learning algorithms. The best performing model was able to distinguish acute from chronic insomnia with an accuracy of 81%. The algorithms were then used to evaluate the acute and chronic groups compared to healthy sleepers. The differences between acute insomnia and healthy sleep were more prominent than between chronic insomnia and healthy sleep. This may be associated with the adaptation of the physiology to prolonged periods of disturbed sleep for individuals with chronic insomnia. The new model is a powerful addition to our suite of machine learning models aiming to pre-screen insomnia at home with wearable devices.