I am trying to test some asset pricing models on 10 portfolios for the period of 2010-2020. The problem is that three of these portfolios included stocks that are newly listed in 2017 and 2018, so I only have three years of historical data for these stocks. Can anyone help how to solve this problem? I don't want to exclude these stocks; does imputation makes sense for such a long period?
I have found some posts to help answer your question. In a post on ResearchGate.net,
One of the responses that I think has the best answer for your is to carry forward the previous data . However, as the person stated, there is a problem with that method. “--- if you are developing a trading system, for example, and assume that prices are "tradable", then your analysis will be flawed since you can't trade at a "carried forward price." My solution to this problem is this: create a 'locf' price and as a separate variable, a "tradable price", which when data is missing, is (approximately) the next price you could have realized. “
However, Mazin A. M. Al Janabi posted a link on that page which has a better answer for you. https://www.researchgate.net/profile/Mazin-Al-Janabi/post/How-to-deal-with-missing-value-in-a-time-series-stock-market-data/attachment/5b73a9633843b0024405fcb1/AS%3A659744100450305%401534306659149/download/Dealing+with+the+Problem+of+Missing+Data-+A+short+Note.pdf He states that you either not include the missing data or you can calculate the price from a geometric mean of the previous and other price data. However using average prices will underestimate the volatility of the stock price data.
Here is another response to a similar question on Stackexchange: https://quant.stackexchange.com/questions/41171/how-to-deal-with-missing-value-in-a-time-series-stock-market-data
I have also posted a similar answer on missing data but not missing stock price data How do I fill gaps in my data?
Either case I think it is VERY important that you document that you have missing data, report which observations are missing, and what method you used to remedy it.