Let's say I have dependent variable (y), independent variable (x1), independent variable (x2).
If y and x1 have the same sample period of 1970 to 2014, but data available for x2 only starts from 1995 to 2014. Can I still regress it anyway? Or I will have to standardize the data to 1995 to 2014? or I shall do extrapolation for x2?
Is 20 years sufficient for time series regression?
I am sure there must be other options but my 1st thought is try step-wise regression. First fit y to x1 & then fit the residual to x2. At they very least, step-wise will give you estimates of the explanatory power of x1 & x2. Perhaps some type of conditional model Bayesian model is possible.
Take all from 1995 and onward that will give better results before that you can analyse separately between the two available leaving the missing one
If you fit the model that explains y as a function of x1 and x2, but the available data for all three variables is only between 1995 until 2014, the remained observations (between 1970 - 1994) will be dropped from the model due to data unavailability. You can either conduct your study only for the available period of time, or you can proceed with an imputation of the missing data.
In your case, that would mean to find at least one variable x3 that is associated with x2, the stronger the association the better, and try to make a prediction for what x2 would have been over the missing interval. You can do this using R software for example, the "mice" package, but be careful with the variable x3 (or the bunch of variables) based on which you will do your imputation. Choose them wisely: otherwise, your results will be totally misleading.
Regarding how long a time series should be for the results to be reliable, there is no "fit to all" answer, as it depends on the process it describes. On financial markets for example, 20 observations are, most likely, insufficient. But if you consider 20 years in a macroeconomic analysis, this interval may capture essential features of your variables. So, it depends.
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