Dear Researchers/Scholars,
Suppose we have time series variable X1, X2 and Y1. where Y1 is dependent on these two. They are more or less linearly related. Data for all these variables are given from 1970 to 2018. We have to forecast values of Y1 for 2040 or 2060 based on these two variables.
What method would you like to suggest (other than a linear regression)?
We have a fact that these series es have a different pattern since 1990. I want to make this 1990-2018 data as prior information and then to find a posterior for Y1. Now, please let me know how to asses this prior distribution?
or any suggestions?
Best Regards,
Abhay
Let me play the devil's advocate:
You have data for the past 50 years. However, you say that there is a mayor break or change in the pattern around 1990, so that you want to use only the more recent 30 years ... to predict what will be in 30 or 50 years in the future?
I doubt that this makes any sense. Toss some dice. It will be as reliable as your model predictions.
If "phase changes" like around 1990 can happen, they can happen in the future, too. Additionally, many other things can happen that we are not even aware of today. The uncertainty about such things must be considerd. Further, as you don't have any model that might be justifed by subject matter arguments, there is a universe of possibilities, again adding to the uncertainty of the prediction. If you consider all this, you will almost surely find that the predcition interval 30 or 50 years ahead will be so wide that it can't have any practical benefit.
You can surely grab one possible model, select some subset of your data, and neglect anything else, then you can make a possibly sufficiently precise forecast, which applies to this model fitted on this data, assuming that nothing else happens or can impact the dependent variable. Nice. But typically practically useless. It's a bit different when you has a model, based on a theory. Then you could at least say that this theory would predict this and that. But if you select a model just because the data looks like it's fitting, you actually have nothing.
It's important to think about all this before you invest a lot of work and time in such projects! It may turn out, in the end, that your approach is still good and helpful. But many such "data-driven forecast models" I have seen in my life have benn completely worthless, pure waste. Good enough to give a useful forecast for the next 2-3 years, but not for decades.
Dear Dr. Jochen Wilhelm Thank you so much for your reply.
I agree with you on the forecasting values for a decade and the underlying uncertainty.
I was just trying for an experiment and comparing the outputs. These forecasts aren't directly involved in decision making (& I agree with your points), but sometimes when someone compels you to see a prediction, we'll have to look for an alternative (just to fix the quest) even though if it has nothing significance in practical.
Best Regards,
Abhay
Well, great, then it does not matter much what you present. No need to spend many thoughts on it. Regress something, predict something. It's good enough if your boss/client feels happy to get something ;)
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