# What date to pick for regression on global stocks

Let's say I have a return of a stock in Japan that I wish to regress on the S&P 500 index using daily data for 1 year. Since the Japanese stock market has different holidays than the US, the dates might not correspond to each other. For example :

US trading dates ->    2008-01-02 2008-01-03 2008-01-04 2008-01-05
Japan trading dates -> 2008-01-01 2008-01-03 2008-01-05


In this case, should the regression be done on the same dates for both markets, thus ignoring the dates that are not identical? Giving us two usable dates: 2008-01-03 2008-01-05. Or is there a better way to do the regression?

• I agree with you that using only the dates on which both markets are open is a reasonable approach. (It is not perfect because the closing times for the tokyo and new york exchanges are 12 hours apart, so you still have a non-simultaneity problem. Some people attempt to reduce that problem by using weekly instead of daily data). – noob2 Jul 15 '20 at 23:23

The way to setup the regression depends on what do you want to predict. Once you formulate exactly what do you want to predict, you should set up your regression in exactly same way.

Daily regression of returns of JPYStock ~ SPX can be done in several ways, and you should consider these differences:

• holidays as you mention
• End of trading day time (i.e. one will be ahead of other, thus there is information leak)
• currencies are different, i.e. you might want to include USDJPY spot FX in your regression

Even if you disregard these differences, and just focus on daily regression (which is basically just estimating Pearson correlation and vols,ignoring FX moves, and accepting that there is information leak), then these holidays differences do not matter if during the holidays period the returns are not abnormal. Estimating correlation over few years, and adding some dozen of non-abnormal returns will not change this correlation significantly. (by adding i mean substituting the returns by 0 if not available on holiday date)

as noob2 mention you might want to calculate this correlation over longer periods, such as weekly, monthly etc. This will change your correlation more than effect of including/excluding same holidays.

• Thanks for your comment. To your point, the JPY stock return is converted in USD and I need to work with daily data, so weekly is not an option. Currently my main concern is the information leak – Circus_beta Jul 16 '20 at 13:03

It is not clear you want to regress changes or indexes themselves? If you regress the indexes, then the 12 hour time difference will not matter. If you regress changes, you better take as the "x" variable the series that leads and as "y" series that lags (by 12 hours). It means that if you want to take d(Nikkei) = a*d(S&P)+b then you want to take the Nikkei change for the next day.