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
In the research with Professor Xu we will be testing on whether the Taylor’s law can be used to predict stock prices. Taylor’s law is one of the quantitative scaling patterns in ecology, and has been confirmed for thousands of biological and non-biological variables. Recent works show that Taylor’s law can be applied to model temporal trends of financial time series. However the predicting power of Taylor’s law for future forecast of time series remains untested.
The goal of our research is to test the empirical validity of various types of Taylor’s law for stock price data and explore the usefulness of Taylor’s law in selecting the best price forecast.
We will be using R as the tool to conduct the research, we will be using the package called Quantmod to get the raw data from yahoo finance for the fortune 100 companies’ stock prices since they went IPO till 3/26/2019 which is the day we started the research.
In this research we will be test three types of Taylor’s law: temporal, ensemble and temporal hierarchical. Temporal Taylor’s law means that we will group the raw data by name and analyze the each stock price fluctuation since they went public. And we would calculate mean and variance for each stock then construct a graph to see if the overall performance is a linear relationship which fit the Taylor’s law.
Ensemble hierarchical, we would group all the data we got by year, so instead of analyze each stock’s overall prices, we analyze the market performance of fortune 100 stock together on a yearly basis, and then calculate mean and variance for each year,so each dot on the graph represent each year.
For temporal hierarchical, we will evaluate each company’s performance individually, different form temporal Taylor’s law, this approach would allow us to look at the change in stock price on a yearly basis.
in addition, we would also make linear regression model for each type of the Taylor’s law based on the mean and variance and determine the overall efficiency of the model