I'm working with time-series data on a handful (about 12) of individuals. Under normal conditions, the variable of interest for each individual is correlated among the group, i.e. if
y is high for one individual, it's high for all individuals and vice versa (However, not necessarily 1:1). There are other variables
x=(x_1,...,x_n) that can influence
y for each individual differently and therefore explain some of the deviation from the group.
The problem: I want to test whether one individual at some point in time deviates from the group for a prolonged period of time, where the deviation cannot be explained by
x. I am essentially looking for a point in time where the value of
y for one individual can no longer be explained by the group. Is there a type of test or model that can achieve this?