Time series forecasting with exogenous variables with VAR and ARIMAX/SARIMAX I have a multivariate time series forecasting exercise with sales data for past one year at daily level along with exogenous variables as number of buyers, price and promotions all at daily level. Say we have sales data from 01-Jan-2021 till 31-Dec-2021 at daily level.
I have to forecast the sales data for next month i.e. Jan-2022 at daily level, i.e. 31 data points, I know one can use VAR/ARIMA/ARIMAX/SARIMAX models to do the forecast for Jan-2022. But my concern is that I already know what price, promotions and number of buyers are for the month of Jan-2022. Now I am not sure how I can include this information in my selected model.
Any help or leads on this would be highly appreciated.

You are probably used to forecasting a target variable $Y_{t+1}$ (univariate or multivariate) given predictors $X_t$ (univariate or multivariate) and $Z_t$ (univariate or multivariate). You do that by
(1) fitting a model with $Y_{t+1}$ as the target variable and $X_t$ and $Z_t$ as predictor variables on historical data and then
(2) feeding the values $x_t$ and $z_t$ into the model to obtain a forecast of $y_{t+1}$.
Now you have $X_{t+1}$ instead of $X_t$, but all else is the same. So just fit a model of $Y_{t+1}$ on $X_{t+1}$ and $Z_t$ and feed in $x_{t+1}$ and $z_t$ to obtain a forecast of $y_{t+1}$. The models to be used for that would be the same as usual (ARIMAX, VAR(X), ...). The only difference is that some lags get shifted, as detailed above.
Also, nowcasting might be a relevant keyword.
