Dementia is a syndrome, generally of a chronic nature characterized by a deterioration in cognitive function, especially in the geriatric population and is severe enough to impact their daily activities. Early diagnosis of dementia is essential to provide timely treatment to alleviate the effects and sometimes to slow the progression of dementia. Speech has been known to provide an indication of a person's cognitive state. The objective of this work is to use speech processing and machine learning techniques to automatically identify the stage of dementia such as mild cognitive impairment (MCI) or Alzheimers disease (AD). Non-linguistic acoustic parameters are used for this purpose, making this a language independent approach. We analyze the patients audio excerpts from a clinician-participant conversations taken from the Pitt corpus of DementiaBank database, to identify the speech parameters that best distinguish between MCI, AD and healthy (HC) speech. We analyze the contribution of various types of acoustic features such as spectral, temporal, cepstral their feature-level fusion and selection towards the identification of dementia stage. Additionally, we compare the performance of using feature-level fusion and score-level fusion. An accuracy of 82% is achieved using score-level fusion with an absolute improvement of 5% over feature-level fusion.