I am looking for a textbook or some other resource where the following multiple linear regression problem is considered.
The model is:
$Y_n = \beta X_n + a+ \epsilon$
Where $\{X_n\}_{n\in\{0,...,T\}}$ are $\mathbb{R}^K$-valued random variables, $\{Y_n\}_{n\in\{0,...,T\}}$ are $\mathbb{R}$-valued random variables. We are therefore looking at the formulation where the regressors are stochastic.
I am interested in the case where the pairs $\{(Y_n,X_n)\}_{n\in\{0,...,T\}}$ are not necessarily i.i.d., but they may satisfy other conditions, for instance stationarity.
The objective is to estimate the parameters $\beta \in \mathbb{R}^K$ and $a\in\mathbb{R}$ given a sample path of the process $\{(Y_n,X_n)\}_{n\in\{0,...,T\}}$.
I have looked into several time-series text books and couldn't find a treatment in this setting.