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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(last 24 hours), and the 10th variable will have the most recent data point from a week or two ago which is quite outdated.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:

  1. 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?
  2. 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like to use past values of the 9 variables and not the past value of the 10th variable as its past value is typically outdated.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the regressors, but also previous value of the regressand which is something I want to avoid as the previous value is outdated.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

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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.

  1. 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).

  2. 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.

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  • $\begingroup$ VAR of order 3. The data is price data. The reason I think it is useless is due to 10th variable prediction not changing much even if other variables double for example. It seems to be mostly attached to its previous value which is outdated. $\endgroup$
    – MilTom
    Feb 23, 2022 at 13:58
  • $\begingroup$ In a most popular soft such as R traditional VAR from vars package assumes that equation for each variable consists of 3 lags of each variable in the system, so building such a model you assume that lags of 10th variable are useful for predicting it's future value. $\endgroup$
    – rsx
    Feb 23, 2022 at 20:39
  • $\begingroup$ I might suggest to move the 10th variable from system, if data for this variable causes so much problems (is this 10th variable important for you?). By the way, you can test whether this variable is useful for forecasting other variables with Granger causality test. $\endgroup$
    – rsx
    Feb 23, 2022 at 20:42
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    $\begingroup$ And I shall mention one more thing. Since VAR coefficients are often unstable and can change significantly after including/excluding new lags or variables to or from the VAR, the important point is common or economic sense you base lag and variable selection on. $\endgroup$
    – rsx
    Feb 23, 2022 at 20:56

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