Regression of stock price, should I include a lagged value of the stock price?

[Sunniva Davidson]

Hi everyone on Statalist,

I am working on a project and have run into a few obstacles.

The purpose of my project is to conduct a multiple regression analysis, with the stock price of an airline company as a dependent variable. For independent variables, I have used Oil Price, Google Trends activity, average temperature deviation in the country where the airline has most of its departures and USD/NOK exchange rate. These variables are all daily variables, and I have included all dates, even though some of the above-mentioned variables do not have values accounting for all dates, such as the weekends for oil price for example.

However, I was wondering if:
1) it makes sense to lag the stock price variable, as the stock price may not immediately react to some of the independent factors? Even though this may be a contradiction to capital market theory; that the stock price always reflect all available information in the market.
2) and if so, how many days does it make sense to lag the stock price?

Thank you so much in advance!

[David Benson]

Hi Sunniva, most daily stock market models do not include the lag of stock price for the reason you mentioned (if markets are efficient it should already be incorporated into the price).

If you are looking to find the market reaction to a specific event (i.e. Delta Airlines acquiring Northwest Airlines) then researchers often include the day before the merger (-1,0) to capture the fact that such news sometimes leaks and the market starts reacting early.

That being said, you could include a one-day lag and see how much it improves the predictive power of your model. Also, you might want to look up "Random Walk Theory" (which argues that yesterday's stock price will have no predictive power on today's stock movement (hence "Random Walk") and is why they view "technical analysis" as essentially voodoo.)