# Estimate correlation of time series whose histories differ in length

Very often in quantitative analysis (e.g. calculating portfolio volatility) we have to analyze various time series - mostly returns - whose lenghts differ.

Risk systems usually apply a one-factor model in order to create a generic history for such time series.

• choose a market index with returns $r_{index}$
• estimate the beta $\beta$ of the time series to this index
• insert $\beta * r_{index,t}$ for all missing dates $t$.

My attention was drawn to the paper Analyzing investments whose histories differ in length by Robert F. Stambaugh. It seems to use a more sophisticated approach.

My question:

• Does anyone here have access to a description of the approach taken by Stambaugh which is not behind a pay-wall?
• What other approaches were published that address this issue?