I want to perform a regression between 3 variables [x1,x2,x3] that have no trend and no seasonality across their time observations and a variable [Y] that has trend and seasonality. For [Y] I've deseasonalized, removed the residuals, then averaged the Trend component values and grouped it by unique combination of x1,x2,x3 observations. Then I ran the regression. The philosophy behind is that changes in x1, x2 x3 affect the trend (slope+absolute) of the variable [Y]
Is it a correct approach or am I mistreating the time series?