In-the-sample regression of HAR model

sometimes some estimators become inefficient.

Table 41: Distribution of R square in Shanghai Markets (15 minute Realized Volatility)

Figure 21: The Ratio of Significant Coefficients

Table 42: How Many Significant Coefficients

According to section 3, 5 minutes realized volatility estimator and 15 minutes

realized volatility estimator is the only two efficient estimators in Shanghai market and Hong Kong market when evaluating realized volatility estimators using 7 years data.

Although 5 minutes realized volatility estimator is regarded as an inefficient estimator on 2011 in Shanghai market, we cannot ignore that it ranks high in other years. As a result, in the following part, we use 5 minutes and 15 minutes realized volatility to do data analysis in the following part.

In Table 40, we find that HAR model can fit Shanghai market well from 2008 to 2014, investors with different horizons are more likely to influence China companies’

stock. In Shanghai market, 71% stocks’ R²s are more than 20%, 1% stocks’ R² are more than 80%, meaning that 32 stocks’ volatilities in Shanghai stock market are heavily driven by 1-day, 1-week and 1-month horizon investors. In Hong Kong market, fewer stocks are driven by investors driven by different horizon, but 15 stocks’ R²s are more than 60%. We check the 32 stocks in Shanghai market and 15 stocks in Hong Kong market. Among 32 stocks in Shanghai market, 27 stocks are industry giants of manufacturing sector or construction sector. The left 5 stocks are 600103.SH, 600186.SH, 600209.SH, 600227.SH, and 600756. All of them were facing debt restructuring, accounting misstatement, false falsification and other financial difficulties. Among the 27 stock in Hong Kong market, all of them are so-called red-chip meaning a China mainland company lists on Hong Kong stock market. Chinese institutional investors are likely to implement government policy by buying and selling index stocks in the stock. From 2008 to 2014, institutional investors keep providing the market with liquidity in China. Among the 64 stocks with low R², we see 31 stocks are local Hong Kong companies.

In Table 41, we can see fewer stocks are with high R². Investors with different horizons are more likely to influence a China company’s stock. When 15 minutes realized volatility is modelled by HAR model, there are more stocks’ R² fell under 0.2.

When the modelled realized volatility is changed from 5 minutes realized volatility to 15 minutes realized volatility, we can see the R² in Shanghai market changes more significantly than that in Hong Kong market does, where stocks with low R² increase from 28.97% to 57.21%, meaning that when we change estimators, the information

including in the estimator also changes seriously in Shanghai market. There are only 12 stocks in Shanghai market left, and 1 stock in Hong Kong market left, with large R². All of the 13 stocks also have large R² when using 5 minutes realized volatility estimator.

But the 5 stocks of whom companies are facing financial difficulties and warned because of accounting misstatement, false falsification disappear from the list.

From Table 42, we see that the 1-month-horizon investors are most consistent investors in both markets. When we use HAR model to model 5 minutes realized volatility estimator, 88.97% stocks’ 1-month-volatlity are significant under 5%

significant level, meaning that 1-month-volatlity is a factor for stock market volatility change. 1-week-volatilty also contributes to stock volatility change in both markets. We can find that when realized volatility estimator is changed, 11% stocks’ 1-week-volatility lose their explanatory power over current 1-week-volatility. In Shanghai market, if we model 15 minutes realized volatility estimator, 1-day-volatlity is not an efficient explanatory variable for volatility.

From the analysis of HAR model, we know that in Shanghai market, 1-day-volaltity does not play a role as significant as 1-week-volatility and 1-month-volatity do. This is partly because high frequency trading need investor taking high risk because of transaction cost and tax, and individual investors do not have the financial strength and knowledge to handle high frequency trading.

The HAR model describe stocks in Shanghai market better. Investors construction of Shanghai market is consistent, because of China financial regulation. Hong Kong is a financial free market, and it is regarded as an destination of financial innovation and risk decentralization. Investors construction in Hong Kong market is volatile, leading difficulties to modelling its volatility.

Table 43: Distribution of R Square in Shanghai Market (5 minutes Realized Volatility)

Table 44: Distribution of R Square in Hong Kong Market (5 minutes Realized Volatility)

Table 45: Distribution of R Square in Shanghai Market (15 minutes Realized Volatility)

Table 46: Distribution of R Square in Hong Kong Market (15 minutes Realized Volatility)

Hence, we use HAR models to gain insight into two realized volatility estimators.

Instead of using a 7-years data before, we use 1-year sampling period.

With sampling period shortened, R² of HAR model in Shanghai market becomes smaller in Shanghai market. When we do regression analysis by 7 years’ data, only 28.97% stocks have R² less than 20% in Shanghai market, but when we analyze data year by year, at least 63.92% R² is less than 20%. When we analyze 15 realized volatility estimator by HAR model, more than 90% R² is less than 20%. Although R² is not the only benchmark to evaluate the model, the low R² always mean the limited explanatory power of a model.

The decrease of R² in Hong Kong market can also be seen from 2008 to 2014. For 5 minutes realized volatility estimator, more than 50% R²s are less than 20%, for 15 minutes realized volatility estimator, more than 70% R²s are less than 20%.

HAR model lose its validity when sampling period shortens. It is not surprising

because investors’ behaviors are variable in short time because of complicated economy environment. Only through long-term observation and correction, can we get the correct parameters.