We collected all the raw data from Yahoo finance.com and combined all the data into one data set.

Firstly,we tested the temporal Taylor’s law by group the data set by company and calculate mean and variance for each one of them so we could evaluate each stock’s performance since they went public. We also built a linear regression model for the mean and variance on a log-log scale to see how the strong the relationship.

This is the mean-variance plot we got for temporal on a log-log scale and we can see it is a linear relationship which matches with Taylor’s law and we can also clearly see some colored outliers which either has significantly high stock price or relatively low stock price. We also test the linear regression model the R-square value which is use to evaluate the strength of the relationship is at around 66% indicates a relatively strong relationship exists between the mean and variance for each stock.

Then we tested the ensemble Taylor’s law which we grouped the data set by year and evaluate the market performance on a yearly basis. From this graph we can observe one interesting thing is that there is push back on year 2008 which is the year when financial crisis happened and we can also see the stock price has been recovering after year 2008 which show us that this Taylor’s law is able to reflect the overall market performance. The strength of this model is 67%.

The last one we tested is the temporal hierarchical Taylor’s law. For this one we will have to group the data set by year and company. Therefore we would be getting the information about how each stock is doing each year and calculate mean and variance of each year for every stock. To clearly see how each stock is doing we built a 5×5 multi-panel and we can see most of the relationship is linear. And the strength of the model is much stronger since there are more variables come into play, the R square is 87%.TH