1. Introduction

As an important indicator of economic and financial activities of a country or region, stock price indexes are of great research importance. The relationship between macroeconomic factors, monetary policy and asset prices has always been the focus of attention in financial economics. The influence of stock price fluctuations is one of the directions that this paper would like to try to analyze and understand. For investors, the analysis of macroeconomic indicators is a very important part. This paper is divided into two parts, the first part is an exploratory data analysis of macro factors and the possibility of some of them having an impact on the HS300 index [1]. The second part is an attempt to learn how to use simply linear regression techniques using the case of individual stocks and the HS300. In addition, this thesis classifies the factors into macro environment indicators [2], such as GDP, CPI, industrial index, etc., and market valuation indicators, such as market average PE, PS, etc. HS300 is used as a benchmark to analyze the correlation between macro factors and HS300 volatility descriptively.

Brasoveanu L O points out that with the development of financial market and securities market, more and more people pay attention to the price movement of stocks and get the factors affecting the movement of stock prices by analyzing the impact of macro and micro economic environment on stock prices [3]. Evangelia Papapetrou argues that these factors include not only the current business situation of the company, but also the trends of the stock industry and the macro economy as a whole [4]. In addition, Li, H. analyses different listed robotics companies and finds that the share of R&D expenses, the growth of GWM and the growth of marketing expenses in the robotics industry have different degrees of influence on stock prices [5]. Zhou, X explores the impact of terms of trade, oil prices, interest rates, money supply and industrial production indices on stock delivery movements through a study of stock markets and firms in the US, Japan and China [6]. Bochen Li takes two emerging Internet companies, Alibaba and Jingdong, as the subjects of his study (using linear regression methods to analyze their stock movements), and then examines the factors influencing the stock market in this industry and provides investors with investment intentions to reduce loss expectation losses [7].

2. Data Profile

Because I have a traditional business background and little understanding of the deep knowledge structure related to statistical mathematics, this paper uses some basic graphs to depict the data as follows.

Data distribution graph: it is to view the data distribution, mainly to determine the normality, skewness kurtosis of the data.

Scatter plot: to view the relationship between data and data; between data and HS300. Mainly looking for linear relationships, and thinking about how to transform non-linear relationships

Heat distribution diagram: view the correlation between data and look for macro factors with strong correlation with HS300

This report’s dataset is obtained from ricequant's stock financial data; Wind's EDB macro database, and information from relevant financial websites. Because sectoral data are lagged, daily data for some indicators are taken with a one-day lag and monthly data are taken with a two-month lag. Quarterly data are only available for GDP and unemployment rate, which are taken with a one-quarter lag. In this paper, we analyze daily data with a one-day lag and use the previous day's data to forecast; monthly data with a one-month lag and use the previous month's end data to forecast.

The types of analysis graphs used in this paper include:

Table 1: Data dictionary.

3. Exploratory Data Analysis (EDA)

First, I think of EDA methods as not just a set of techniques or functions or graphs, but as an attitude/philosophy about how to do data analysis. EDA is a data analysis method that infers the usual assumptions about what models the data follow by allowing the data itself to reveal its underlying structure and model in a more direct way [8]. Besides, EDA is not just a collection of techniques., but it is a philosophy about how we dissect EDA is a philosophy about how we dissect datasets; what we are looking for; what they look like; and how we can better explain their intrinsic connections. It is true that EDA makes extensive use of a collection of techniques we call "statistical graphics," but it is not exactly the same as statistical graphics themselves(see Table 1).

Most EDA techniques are inherently graphical, with some quantitative techniques. The reason for this heavy reliance on graphs is that EDA's primary role is essentially open to exploration, and graphs give analysts an unparalleled ability to explore, to entice data to reveal its structural secrets, and to be ready to gain some new, often unexpected, insight into the data. Combined with the natural pattern recognition capabilities we all possess graphs certainly provide an unparalleled ability to do just that.

Thus, the first step of doing data analysis is to find out the missing data, distortion, and misrepresentation; after that, the integrity of data usage is ensured by cleaning and filling the data. Last, the real relationship between the data has to be found so that a suitable model can be selected. The following steps are the data analysis done in this project.

3.1. View Missing Values

The data processing starts with the missing data, which are listed below in Table 2.

Table 2: Dictionary of missing values.

Figure 1: Stock factor categories.

From the Figure 1 shows that the total data volume is 3150, the fixed investment data ('fixed_assets_investment') and retail sales data ('retain_sin') are the most missing. The industrial ex-factory indexes ('ppi', 'food', 'clothing') also have missing values for almost 4 months or so, while other data such as ( pmi, import) are missing for less than two months. By studying the macro database I found that: fixed investment data ('fixed_assets_investment') data do not include all January data; retail sales data ('retain_sin') do not include Data for January and April after 2011, which account for the bulk of the missing values. The industrial ex-factory index is occasionally missing data for one or two months in the last 10 years, and there are some missing data. In addition, looking at the database, I also found that there are many cases of NaN in the Ex-Industrial Index database, which should be noted in the data cleaning. Finally, the missing data of pmi, import and so on are caused by the current time of this month and the previous month data are not entered; the missing data of open and close are caused by the missing data of open and close of CSI 300 in January-April 2005.

In terms of missing data treatment, for the missing issue of opening and closing prices in January-April 2015, this thesis removes this data and does not count it in the data sample; for 'fixed_assets_investment', 'retain_sin ' and other data in the industrial ex-factory index PPI library, this thesis replaces them with data from the previous month; finally December and November 2017 are not counted in the data sample analysis to deal with the missing values of pmi, import and other data.

3.2. Distribution of Data Values

I need to analyze the distribution of HS300 price data to know the overall situation of the data, the distribution chart is as follows

Figure 2: HS300 data distribution.

The Figure 2 shows the skewness and kurtosis of the price distribution are calculated as

kewness: close 0.175869

kurtosis: close 0.341954

The skewness of 0.175869 indicates that the prices are slightly skewed to the right; the kurtosis of 0.341954 indicates that the kurtosis is not high. Because the skewness of the normal distribution is 0 and the kurtosis is 3, while the kurtosis of the stock price of HS300 differs greatly from the normal distribution, it can be judged that the stock price of HS300 does not obey the normal distribution. The stock index probability distribution is not on the red mean, the highs are skewed high and the lows are skewed low. Next, the distribution of the daily growth of HS300 is analyzed as shown below

Figure 3: HS300 daily price change distribution.

The Figure 3 illustrates the price changes (Change_rate) skewness kurtosis are-0.278169 and 4.178902. The skewness is -0.278169, which means that the price is slightly to the left and the center of gravity is to the right; the mean value is around 0; the kurtosis is 4.178902, which is close to the normal distribution. It is not possible to have a linear correlation with the stock price.

3.3. Single Factor Analysis

Figure 4: Single-factor distribution.

The Figure 4 shows different single-factor analysis and data distribution.

PB: PB is right biased, the center of gravity is on the left, and the kurtosis is also slightly higher, so it can be log transformed to make it conform to unbounded Johnson distribution, and it can also be standardized.

PCF: PCF almost no skewness, kurtosis is very high, not suitable for standardization operation, but can reduce its kurtosis, but because the traditional method of reducing kurtosis log is not good for the case with negative numbers, you can first pan with the minimum value, and then log

PE: skewness is positive, the magnitude is not large; kurtosis is high, but not particularly high, you can log processing to adjust the skewness

PS: the skewness is positive, the magnitude is not large, the kurtosis is similar to the normal distribution, no need to deal with

pmi: higher kurtosis, can do log processing, less need for special processing

turnover ratio: The extreme value of 3% for each of the maximum and minimum is deleted when calculating the market mean. turnover_ratio distribution skewness is positive, the magnitude is large, can be log processed

Macroeconomic index (leading index) leading_idx: does not obey normal distribution, but its distribution is extremely similar to HS300 stock price distribution, which may have a strong linear relationship.

Total retail sales of social consumer goods retail_sin: the skewness is positive, the magnitude is not big, the kurtosis is not big, can't see what special treatment is needed.

Fixed asset investment completion (cumulative year-on-year): positive skewness, high kurtosis, not suitable for log to reduce skewness due to a large number of values around 0. This factor is not meaningful to use directly, and I would like to try to use proportional change as a substitute.

Figure 5: single-factor distribution.

CPI: right skewed skewness, high kurtosis, suitable for log processing

M1: It is recommended to represent the data with change proportion

M2: Suggest to use the change proportion to represent the data

Unemployment rate URUR: The data comes from Wind database, the data is obviously not in line with common sense, according to the unemployment rate of the United States or other countries, the unemployment rate should fluctuate around 3%-8% is more normal, during the economic crisis may exceed 10%, a major economic crisis such as the 1932 economic crisis may be more than 20%. 2005 to 2017 12 years there was a major financial crisis. The time span is also very large, but the unemployment rate fluctuates but not more than five thousandths, the data distortion is serious(see Figure 5).

Total imports IMPORT: not normally distributed, but similar to the stock price distribution, probably linearly related to the stock price

Total exports EXPORT: the same as above, and the import correlation may be very large

Total import and export TOTAL: same as above

Import year-on-year IMPORTYOY: probably right skewed, with high kurtosis, can do log processing.

Exports year-on-year EXPORTYOY: left skewed, higher kurtosis, can do log processing or square processing. Compared with imports, there are few values higher than 50, which means that the increase is steady and there is no sudden big leap.

3.4. Heat Map

Heat map, a statistical chart that displays data by coloring blocks of color. When plotting, rules for color mapping need to be specified. For example, larger values are represented by darker colors and smaller values by lighter colors; larger values are represented by warmer colors and smaller values by cooler colors, etc. The advantage of heat maps is that they are "space efficient" and can accommodate relatively large amounts of data. Heat maps are not only useful for discovering relationships between data and finding extreme values, but they are also often used to paint a picture of the data as a whole and facilitate comparisons between data sets. Thus, the 30 most important factors for stock prices were selected because log and sqrt were used, and there were duplicate values in them, which actually took about 10 important variables. The group also tried to organize the data by standardized methods, but the results were poor on the factors with high importance, so these factors were deleted.

Figure 6: Stock factors correlation analysis.

According to the Figure 6 heat map it can be seen that the financial data of the company are more correlated with each other, other macro data are more correlated with each other and less correlated with both parts of the data. It is worth noting that CPI has a low correlation with exports, M1 and M2 macro data indicators, and even has a negative linear relationship of 20% with “retail_sin”. However, CPI has a high positive correlation with consumer “dcg”(durables price index).

4. Linear Regression Analysis

The HS300 index is jointly compiled by Shanghai Stock Exchange and Shenzhen Stock Exchange, and the sample covers about 60% of the market capitalization of Shanghai and Shenzhen markets, which has good market representativeness. Therefore, in addition to the exploratory analysis of HS300 related factors, this paper also investigates whether there is a linear relationship between the stock prices of individual stocks and HS300, and tries to conduct correlation analysis based on the OLS regressions learned in the course.

4.1. Data Describe

Table 3: Data descriptive statistics.

The Table 3 simple statistics of the closing price of HS300 for each trading day in the statistical interval, are Figure 7 shown below. There are 146 HS300 share price data, the average value of the share price is 3864.70, the minimum value is 3025.69 and the maximum value is 5353.75. And the simple statistics of the closing price of Robotics for each trading day are shown below. There are 146 share price data, the average value of the share price is 78.942740, the minimum value is 48.280000, and the maximum value is 128.0

Figure 7: HS300 index&robot company volatility distribution.

We can observe that Figure 7 shows the stock price volatility of HS300 and Robotics, as shown above, has a relatively consistent trend between the stock price volatility of HS300 and Robotics, while Robotics has a more volatile stock price compared to HS300.

Figure 8: HS300 index&robot company daily returns distribution.

Drawing the histogram and density plot of daily returns of HS300 and Robotics, as Figure 8 shown above, it can be found that, in general, the daily returns of HS300 and Robotics obey normal distribution. Comparatively, the daily return of robotics companies is lower than that of HS300.

Figure 9: HS300 index&robot company correlation distribution.

The Figure 9 scatter plot shows that there may be a linear positive correlation between HS300 and Robotics' stock price.

4.2. Regression Results

Linear regression is a data analysis technique that predicts the value of an unknown data by using another relevant known data value [9]. It mathematically models the unknown or dependent variable and the known or independent variables as linear equations. Essentially, a simple linear regression technique attempts to plot a line graph between two data variables x and y. As the independent variable, x is plotted along the horizontal axis. The independent variable is also called the explanatory or predictive variable. The dependent variable y is plotted on the vertical axis. The y value can also be indexed as a response or predictor variable.

Since my own background is in Business, I am familiar with the framework of investment reasoning and value investing, not really good at math or data engineering oriented content. After several weeks of lectures, I tried to use a simple regression model to analyze the correlation between the HS300 and individual stock relationships.

Table 4: OLS regression results.

The Table 4 least squares regression results show that there is a significant positive relationship between the daily stock returns of robotics companies and the HS300 daily returns. The decidable coefficient is 0.457, indicating that the HS300 daily return variable has a strong explanatory power on the robotics daily return variable and the model fits well. p-values for both the F-statistic and Omnibus statistic are close to 0, and the effect of the independent variable is significant. p-values for the t-statistic are close to 0, indicating that the HS300 variable is significant. The coefficient of the independent variable is 1.3137, indicating that the daily return of the stock of Robotics is more volatile than HS300 and that the individual stock is riskier and has greater potential for gains and losses. The average HS300 daily return fluctuates by 1% and the individual stock daily return fluctuates by 1.3137 %. the value of the Durbin-Waston test is 1.952, indicating that there is no serial correlation in the return data.

5. Conclusion

With the development of globalization of capital market, the importance of Chinese securities market in the international capital market has become more and more prominent. Pham, T. A think the Asian capital market is developing at a rapid pace and that the stock market is a very important part of the capital market When different price indices (HS300) are designed, investors will have more underlying objects to study financial market liquidity, systemic risk and stock price volatility [10]. The research in this paper includes an exploratory analysis of macroeconomic indicators and finds that some factors such as: PB, PE, pmi CPI retail sales of social consumer goods, turnover ratio, etc. have a correlation effect on the HS300 index. In addition, this paper does a simple linear regression analysis on the share price data of individual stocks (robotics companies) and the closing price data of HS300, and the results have a linear relationship.