## Blog 4

This academic year, I had an great opportunity to conduct research with Dr.Xu. Our goal of this research was to see if Taylor’s law is able to forecast the future stock prices and if it is possible which type of Taylor’s law produces the most power projection. During this research, time management was definitely a challenge for me,since I have both school work and internship to care about also. But from this semester’s experience, I did learn a lot about how to balance things out.

During this research project, since we are using R(programming language)as the researching tool, I need learn more about R on my own to know what function and what package would be useful for my research. In addition, I have learned more statistics concept throughout this research, such as exponential smoothing, ARIMA model, and etc.

For the outcome of our research, we have started using some more advanced model in order to forecast future stock prices. However one of the disadvantage of those model is that we cannot predict unforeseen situation that has great impact on the market such as the COVID-19 situation. So our goal is to predict the market price if the market still operate as normal.

## Blog 3

During the winter break, I was able to make some new progress on my research. After I built regression model for all three of the Taylor’s law, I observed that temporal Hierarchical has the highest R-square which means it is the strongest model out of the three Taylor’s law.

I have also done some improvement on the temporal hierarchical model, instead of calculating the mean and variance as a whole, I use the DO function in R to calculate mean and variance relationship for each stock individually to reflect which stock has the strongest correlation between mean and variance.

I have strated to do some forecasting such as naive method, drift method and average method. I will first do a five year forecasting on data from 2015 to see if the forecasting is valid

## Blog #2

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

## Blog 1: Can we use Taylor’s law of fluctuation scaling to select the most feasible time series forecast of stock prices of Fortune 100 companies?

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