# Recursive time series forecasting model

In a recursive forecasting model, let's say you are trying to predict sales of Target for the next month and you will append that prediction to your input and predict the month after. Basically, your target is Sales quantity, which you lagged. But let's say you have other continuous numerical features like Price which you will lag as well. As your model is making predictions on Sales_QTY, it will feed it back to sales_qty as input so you will never ran out of values for that one. So how do you deal with your other features (other than the target) in order to generate them as next months inputs in a recursive forecasting model (because eventually you will run out of them)? DO you create a sub-model and try to predict them as well?

• You could try to predict them with another model or use some other measure like the average or last value. You could also do some simulations with multiple different values and average the results. Jun 11 '21 at 18:54
• I tried both techniques but I was looking for something better Jun 11 '21 at 19:14
• stats.stackexchange.com/search?q=user%3A3382+sam+savage might give you some help in encoding uncertainty in future values of the predictor series. This is a feature of AUTOBOX a time series forecasting system that I have helped to develop. Jun 13 '21 at 16:24
• What do you think about my answer? If it is helpful and clear, you may accept it by clicking on the tick mark to the left. Otherwise, you may ask for further clarification. This is how Cross Validated works. Jul 13 '21 at 9:58

A standard approach would be to train direct multi-step models (DMS) for each forecast step instead of a recursive model. So you would train one model to predict $$y_{t+1}$$, another model to predict $$y_{t+2}$$ and so on.

• no need to forecast additional variables that might be hard to forecast, e.g. stock level
• no mix-up between actuals and predictions
• short-term models can use different variables than the long-term models, e.g. today's sales and stock is important for the short-term models, but general trends and product lifecycle are more important for the long-term models

I tried both techniques but I was looking for something better

There is no magic way around the fact that the future values of explanatory variables are unknown, just as the future values of the variable of direct interest are unknown. You could use a vector autoregression to forecast all of the variables together or (as Tylerr suggested) have individual predictive models for each variable. Or if you have expert forecasts available, you could use those, too.

Also, note what Chris Haug points out: including an explanatory variable that is hard to forecast is not guaranteed to improve the forecast of the variable of direct interest. Only if you can forecast the explanatory variable with sufficient precision may it be worth retaining it in the predictive model.

• Thankyou very for the suggestions. That helps. Jun 11 '21 at 20:15
• You could also simply drop the explanatory variable: if it's just as hard to forecast as your target, you might not gain anything at all by including it, even if they are strongly related. Jun 11 '21 at 21:24
• Monte Carlo schemes to incorporate uncertainty in future exogenous series has been incorporated in products like AUTOBOX using suggestions from Prof. Sam Savage author of "The flaw of averages" Jun 13 '21 at 16:20