I have a dependent variable, $Y$, which is made up of several independent uncertain variables, $X$. Independent variables are dependent to each other and there are co-variance and spillover effects between them.
The first question (the most general one) is: how $Y$ can be constituted from $X$?
In addition, according to my studied, auto-regression models may be helpful to represent interactions between dependent and/or independent variables, but these models require observed data for $Y$ and $X$ to calculate the model parameters. Hence, the second question is: in situations that data gathering is not possible, is it reasonable in auto-regression models to replace independent variables with uncertain variables following a specific probability distribution and estimate their values by a given confidence interval?
The last question is: if gathering data is possible and the auto-regression model will be estimated, is $Y$ an uncertain variable? if yes, how its probability distribution can be determined?
Thanks for your helps in advance.