I have 2 stochastic times series $(X_t)$, $(Y_t)$. I would like to calculate the following quantity :
$$\Bbb E[ X_{(t+1)} \mid Y_t,t ]$$
Expectation of $(X)$ at time $(t+1)$ conditionned on values of $(Y_t, t)$.
Empirically, do I need to calculate the bivariate distribution of $(X_t,Y_t)$ as well the marginal distribution of $(X_t)$ ?
Also, tried to find some research on conditionnal time series, but could not find any ressource (apart the time series conditionned on itself at previous dates).