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I am not sure if this is the right place to ask this question. Anyway, I am working on a Forecasting using spending data. Using autoregression, I am able to predict the following number decently well but I would like to improve this. I have two other factors that don't predict nearly as well as the lagged factor but could still be useful in the model.

My question is this: would it be valid to include those factors in the model even though I am using a lagged version of the predictor? Does an autoregression imply that the only factor to be used is the lagged version of the predicted value?

I can't show the data as it is sensitive and my question is more about how autoregression and forecasting work in general.

Thanks for any help.

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The idea of adding external variables is not new. ARIMAX model (https://robjhyndman.com/hyndsight/arimax/) was specifically created to include them.

If you ask whether it is ok to include the external variables of some particular period then the answer is that you need to understand when they are available for prediction. If you predict a profit of the company at an end of a year based on today's stock price then it is ok. The profit and loss statement appear much later than the information is available in stock price. And stock price should have some info on expected profits based on the financial theory. If you want to predict tomorrow's stock price based on tomorrow's number of sun spots then it is a bad idea. The number of sun spots tomorrow is not available today.

And generally you can use any combination of lags for different variables. Taking today's stock price and last year's profit to predict this year's profit is totally valid and even has financial theory supporting the relationship.

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