conditionnal time series

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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).