# Grand Theft Autocorrelation

In my last post, I discussed the concept of correlation. In my free time since then, I’ve been playing a lot of Grand Theft Auto V. It’s time to merge these noble pursuits.

As you may know, GTA V includes an online stock market that allows players to invest their ill-gotten gains in fictitious companies. Naturally, a Reddit user has created an updating database of Stock Market prices. I play on a 360, so I’ve analyzed the Xbox prices. I’ve developed a strategy that will earn money in the long-run, but first let’s do some learning.

As we previously discussed, correlation is a measure of how well the highs of one series line up with the highs of another series. Autocorrelation is a measure of how well highs of a series line up with the highs of the previous observation of the same series.

One could study the correlation of the temperature in Houston vs. the temperature in Austin. One would study the autocorrelation between yesterday’s temperature in Houston and today’s temperature in Houston.

One can study autocorrelation at different “windows” of time. A window of 2 would instead compare today’s temperature to the day after tomorrow.

One obvious question to ask about the GTA stock market is whether there is autocorrelation in returns. If so, then buying companies that just had gains will, more often than not, lead to additional gains.

There isn’t an autocorrelation function in Excel, but one can easily create one by either nesting OFFSET() in CORREL() or by arranging CORREL() ranges like this:

In the attached workbook, I first organized the data to show the closing price for each day and stock. I then computed the log-return for each day and ran autocorrelation on a 1 and 2 day window. I only had complete data for 20 days, but I was able to analyze all 39 stocks, so there was a fairly large amount of data points (N=702 and N=663 for the 1- and 2-day window).

I found a surprisingly high amount of autocorrelation on even the two day window:

Here’s a graphical analysis of the 1-day window. Each point represents a single observation. The x-axis is equal to the previous day’s log-return. The y-axis is equal to the next day’s log-return. The solid line represents the best-fit linear relationship. The second coefficient is significantly close to zero, so I would expect we are very close to a fundamental law of the GTA V market. This doesn’t feel like the result of player behavior.

It appears as though a good estimate of today’s log-return is yesterday’s log-return times 0.637. This simple model is able to explain 44.13% of the observed variance in returns.

In short, ride bandwagons.

This analysis could be extended by analyzing data on an intraday rather than a daily basis, (in the future) adding additional days, seeing if the autocorrelation parameter is consistent across stocks, seeing if individual stock returns are correlated with the market as a whole and seeing if competing stocks display negative correlation. All utilized data and calculations can be downloaded from this workbook.

In future posts, I will perform this same analysis on real stock markets and see if they can be exploited by similar trading strategies. Until then, enjoy the city of Los Santos.