  Changepoint detection is the problem of finding abrupt or gradual changes in
time series data when the distribution of the time series changes
significantly. There are many sophisticated statistical algorithms for solving
changepoint detection problem, although there is not much work devoted towards
gradual changepoints as compared to abrupt ones. Here we present a new approach
to solve changepoint detection problem using fuzzy rough set theory which is
able to detect such gradual changepoints. An expression for the rough-fuzzy
estimate of changepoints is derived along with its mathematical properties
concerning fast computation. In a statistical hypothesis testing framework,
asymptotic distribution of the proposed statistic on both single and multiple
changepoints is derived under null hypothesis enabling multiple changepoint
detection. Extensive simulation studies have been performed to investigate how
simple crude statistical measures of disparity can be subjected to improve
their efficiency in estimation of gradual changepoints. Also, the said
rough-fuzzy estimate is robust to signal-to-noise ratio, high degree of
fuzziness in true changepoints and also to hyper parameter values. Simulation
studies reveal that the proposed method beats other fuzzy methods and also
popular crisp methods like WBS, PELT and BOCD in detecting gradual
changepoints. The applicability of the estimate is demonstrated using multiple
real-life datasets including Covid-19. We have developed the python package
"roufcp" for broader dissemination of the methods.
