Regression of TAQ half-hourly stock volume data against news volume

Question

I am planning to run regression of half-hourly stock volume against the half-hourly news volume for that particular stock. I am looking at 2 years of data for my analysis. However, I am stuck thinking about what should be done to the non-trading hours period on each day?

To be specific: 1. Should I regress the data only for the working hour of the exchange, which means that the Y -values in my regression will contain the "stock volume" in each 30 minutes from 9:30-16:00 on each day from start date to the end date of my regression period and X-values will be the corresponding "news volume" in each 30 minutes?

OR

1. Do I need to make the data evenly spaced in 30 minutes and include the "non-trading hours" for each day with "zeros" as the stock volume and the news volume?

I believe the regression result will be different in both the cases. Need an urgent advise.

Answer 1

Do not run the zeros against the zeros. This is similar to how weekends are treated in academic studies. There is not five days with two additional days of 0 in the regressions for each week in the sample... there is just the five days (although I do encourage you to read about the weekend effect).

Your hypothesis is that there exists a function $Volume(t) = f(News(t)) + e(t)$. When the market is closed, no such function can exist, so what are you supposedly estimating with the zeros in the regression equation? If you include the zeroes, then what you are saying to the model is that during these times $Volume(t)=0$ because $News(t)=0$. Yet we know this is false, and that they are both zero because $t \in \{Market Close\}$.

If you are really concerned about the irregularly spaced time series, you could consider a more legitimate data generating process:

$$ Volume(t) = f(News(t))*I(t \in \{Market Open\}) + c*I(t \in \{Market Close\}) + e(t)$$

where $I$ is an indicator function. However you will notice that this will give you identical parameter estimates (if $f$ is linear with an intercept) as if you simply estimated the original equation during trading hours only.