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I have a VAR model for forecasting in which there is a particular variable $X$. The time series for all the other 7 variables stretches back to 1980 and ends at the third quarter of 2023. Now, $X$ does not have an observation for the third quarter of 2023. So, $X$ is missing an observation for the latest and last data point.

Is there a way to deal with this? Is there a proper way to estimate the last observation value of $X$ to fill in the missing value?

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You could model $X_t$ using linear regression with lags of $X$ and contemporary as well as lagged values of all other variables as regressors. E.g. in a bivariate model, $$ X_t=c+a_{0,2}Y_t+a_{1,1}X_{t-1}+a_{1,2}Y_{t-1}+\dots+a_{p,1}X_{t-p}+a_{p,2}Y_{t-p}+\varepsilon_{t}. $$

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