This study presents a novel threshold algorithm that is applied to daily self-measured SpO2 data for management of COPD patients in remote patient monitoring to improve accuracy of detection of exacerbation. Conventional approaches based on a fixed threshold applied to a single SpO2 reading result in high false alarm rates. We model the SpO2 time series data as a combination of a trend and a stochastic component (residual) and use the standard deviation of residuals to identify exacerbations. Deterioration in the condition of a patient results in an increase in the standard deviation of the residual (σres), from 2% or less when the patient is in a healthy condition to 4% or more when the condition deteriorates. We present results from retrospective analysis of SpO2 data measured in patients with COPD as part of a long term project to monitor frail elderly, and compare results from the new approach with those from the conventional approach.