Principled way of combining time series with different spans and granularity into an econometric model I want to forecast the price of something given various time series as inputs. The problem is that they are of different frequency (annual, quarterly, monthly, daily) and time periods (the more granular ones only cover the recent past). It would be a shame to merely consider the intersection of them all and discard the rest. I'm not used to modeling time series for econometrics, but I assume these are common problems, so what are the standard solutions?
 A: In terms of the frequencies I usually use the highest possible. For instance, if I'm working with GDP and Unemployment, I'll use monthly frequency. GDP is usually quoted as annualized growth rate (continuous compounding), so you can keep it constant for all three months of a quarter. If you are using Disposable Income, it's usually in $ amounts, so you can divide it by 3 and keep it constant during the quarter. 
Be careful with linear interpolation. It's tempting to interpolate GDP growth rates, but it would be incorrect. You will not be able to recover GDP from interpolated rates. You have to keep them constant.
Also be careful with continuous and simple compounding. The former can be kept constant, the latter when increasing the frequency must be properly transformed using powers and roots.
Dealing with data of different lengths is more difficult. Usual tools like OLS and VAR do not work very well in this case, you have to create the intersection data set. State-space methods are much better in handling the missing data. You may want to re-cast your time-series models in state-space representation to deal with this.
There are other issues with different sample sizes. Let's say you are estimating the correlation matrix and your variables have different sample sizes. In this case the resulting matrix may end up being non-positive definite. There are ways fixing this issue too.
