Prediction with VAR where a variable has no recent data I have 10 variables for which I do one-step ahead forecast using a VAR model. The model was trained on historical data for the variables.
Almost all the variables receive new data points daily, so each time a new value comes in for any variable I make a new forecast and at the moment I do not use predictions as lags, only the most recent value for each variable.
Data for one of the variables comes quite infrequently, so in my prediction equation I would have quite recent data for 9 variables (last 24 hours), and the 10th variable will have the most recent data point from a week or two ago which is quite outdated.
What are my options here? I was thinking of either:

*

*Using the prediction value for the 10th variable as the input in the lag for the next prediction and for all other variables use the actual incoming values, since they come frequently. I am afraid here of growing errors as each prediction has an error associated with it. Is my concern valid?

*Use another multivariate model to predict only the 10th variable having other 9 variables as regressors. The key here is that I would like to use past values of the 9 variables and not the past value of the 10th variable as its past value is typically outdated. What model could I be looking for here? From my understanding ARIMAX requires not only the values for the regressors, but also previous value of the regressand which is something I want to avoid as the previous value is outdated.

Thanks

Could you please provide a bit more details about model and data? Is your VAR order 1? And why do you consider lags of the 10th variable to be useless to predict its most current value?
Yes, you can use multivariate or univariate model to predict the value of the 10th variable which is not observed.

*

*Univariate models: typical are ARIMA or ETS. But they are built under assumption that previous data is useful for forecasting future values, and you say it's not truth. You can also make forecast equal to last observable value of the 10th variable (such a forecast is build under assumption of unit root in series and is often used as benchmark for more sophisticated model).


*Multivariate models:
2.1 ARIMAX (ARIMA with exogenous regressors, uses AR and MA lags, assumes previous observations are useful for predicting future values).
2.2 VAR (as you considered, and you have already fitted it).Prediction based on actual values of 9 variables and prediction for 10th may contain error, but you can check on test sample whether this error is acceptable or not.
2.3 If variables are nonstationary and there exists linear relationship between them (cointegration), you might fit VECM model and use it to forecast 10th variable.
If your task is to produce most accurate forecast, just compare different options by their errors on test sample.
