Can I use a cumulative variable that sums up previous observations as a dependent variable in an OLS regression? I am writing my thesis where I am analyzing the effect of tweet sentiment on abnormal stock returns for companies during an event of negative press.
My dataset comprises of various negative press events for different companies for an event window of 7 days (t = -7 to t = 7), where for each event I measure abnormal returns per day, cumulative abnormal returns (CAR) per day, and the average tweet sentiment of that day.
My regression formula currently looks like this:
abnormal returns ~ Tn * sentiment + Tz * sentiment + Tp * sentiment
where:
Tn = abs(t) if t is negative, otherwise 0
Tz = 1 if t=0 (event day), otherwise 0
Tp = abs(t) is t is positive, otherwise 0

Running this regression gave me no significant coefficients, however when I used CAR as my dependent, I got a significant coefficient for the Tp var, and the sentiment:Tp var.
My question is, is it statistically wrong to use CAR as a dependent variable, as the individual observations are not independent from one another, all else equal? Or is it still valid?

The cumulative variable has no errors that are independently distributed. Ordinary least squares (OLS) makes this assumption and if it is violated then you over-estimate the precision of your fitted curve. You should use generalized least squares (GLS) instead, to involve the correlation between the error terms.
