**market**index on the Shanghai Stock Exchange, the Shanghai government bond market index yield not only has the characteristics of non-normality and conditional heteroscedasticity, also has a long memory characteristics. Empirical studies have shown that FIGARCH (1, d, 1) model can portray the volatility of the Shanghai Stock Exchange Government Bond Index yield characteristics.

Keywords: non-normal sexual; conditional heteroskedasticity; Long Memory; FIGARCH (1, d, 1) model

A question and Literature Review

Financial time series, such as yield time series often have time-varying characteristics and beam trends, the variance will change over time and change, showing heteroscedasticity features. Therefore, the characterization of financial time series, mainstream research methods are built on the basis of the ARCH model.

Study abroad, Brooks and Simon (1998), selected according to certain criteria specific GARCH model to predict the volatility of the U.S. dollar; Aguilar, Nydahl (2000) use GARCH model for modeling the volatility of the exchange rate, and achieved better fitting effect; Torhen Bollerslev 'et al (2001), based on the value of the German mark and the Japanese yen against the U.S. dollar, the daily exchange rate value, based on fluctuations in the distribution and correlation of the daily exchange rate, and improve the GARCH model Using the sample distribution restrictions.

In China, the Hui Hillsborough (2003) to predict the RMB exchange rate based on time series GARCH model found GARCH model to forecast the exchange rate and the real exchange rate is very close to the fitted curve almost completely to keep up with the trend of the real exchange rate; Zou Jianjun (2003 GARCH (1,1) model has better estimate and predict the effect of earnings volatility in Shanghai) study found. Cattle Fang Lei, The Un-Canton (2005) use ARCH model fund market volatility conducted the study, found that SSE Fund Index yield performance of the non-positive normality and conditions different variance of characteristics GARCH (1,1) model SSE Fund fluctuations in the fitting. Wang Jiani,, Wenhao Li (2005) Application ARCH Models 1999-2004 euro, Japanese yen, British pound, Australian dollar and four currencies against the U.S. dollar exchange rate.

These studies show that the ARCH class model can accurately portray the financial time series, in particular, the volatility of the financial yield time series. Therefore, China's exchange bond market volatility, the ARCH model based-depth analysis of the exchange bond market volatility inherent characteristics, select the appropriate model to portray.

Second, sample selection and statistical characteristics analysis

(A) sample selection and indicators designed

Shanghai Bourse index basically reflects the overall changes in the Shanghai Stock Exchange, Treasury prices. SSE Government Bond Index as a research object herein above, select the February 24, 2003 to 2006, 18 Daily SSE Government Bond Index closing price for the sample, a total of 764 observations, data from the Shanghai Stock Exchange, Xiangcai securities rotary screen and other related sites.

Determine the sample of the study period, the Japanese yield SSE Government Bond Index calculated, is calculated as follows:

OX locale TSM0.4 package calculated.

(B) the statistical description and analysis

First, based on the sample sequence (see Figure 1), its basic fluctuation characteristics were analyzed, followed by autocorrelation test the unit root test, test of normality and heteroscedasticity test. The results are as follows:

(1) according to the Ljung-Box Q statistic and the corresponding P values ??(see Table 1), we can determine the sequence of samples are delayed at least 25 during the period, no autocorrelation null hypothesis can not refuse, the sample sequence autocorrelation.

(2) the sample sequence ADF unit root test and inspection select impermanence number and trend type sequence fluctuate around zero mean t-statistic for the ADF test -14.69335, significantly less than the significance level of 1 % -3.4415 Mackinnon critical value, indicating that at the 1% level of significance, reject the the sample sequence exists unit root null hypothesis, the sample sequence has stationarity.

(3) The peak degree (K), skewness (S), and JB test the normality of the joint judgment sample sequence (see Table 2), the results show that the sample sequence is significantly different from a normal distribution, peak thick tail phenomenon.

(4) test sample sequences heteroscedasticity, ARCH-LM test, take a lag order of 1 results (see Table 3) show the sample sequence l% significance level, the residual sequence exists ARCH effect, indicating the sample sequence heteroscedasticity, when the lag order to take 10, 20, and the results are consistent.

Secondly, based on the sample sequence since the related ACF Figure lag order of 200 (see Figure 2), the sample sequence memory characteristics analysis, we can find 11 steps down before the autocorrelation function quickly, and subsequently slow attenuation, until the 141 order to gradually close to 0, visible autocorrelation function has a strong dependence on the previous impact, but also in the form of its attenuation is not quickly decay exponentially and slow decay, but in the form of a hyperbola, This indicates that the impact of the conditional variance has a very long lasting, and a sequence of samples having a long memory characterized using standard GPH inspection. GPH-estimator in accordance with standard samples derived sequence memory parameter d = 0.43215 (0.0162), brackets for OLS estimated P value of the test statistic, the results clearly show that the presence of a long memory characteristics of the sample sequence.

Third, the Shanghai Stock Exchange government bond yields and volatility models

First sequence samples yield auxiliary regression model:

General financial literature GARCH (1,1) model is able to describe a lot of financial time series data, According FIGARCH (1, d, 1) model conditional heteroskedasticity sample sequence modeling, model final form :

Fourth, empirical research

(A) parameter estimation

Model parameter estimation method using pseudo maximum likelihood estimation (QMLE). Fractional difference operator d is to capture the features of the process and long-term memory, parameter estimation, the lag order optional 200 order. In addition, because the sample sequence has a non-normal characteristics This article assumes that the residual series in the parameter estimation process obey the t-distribution. Calculation results as shown in Table 4:

Model AIC value -12.314 SC = -12.243, are very small, indicating that FIGARCH model can fit the data. In addition, the use of the Box-Pierce statistic, further standardized test model varies sequence and whether there is autocorrelation sequence, where K is the lag order, take k = 20, come to the Q (K) = 6.32 (0 .914), Q

^{ 2 }(20) = 16.72 (0.923). The results are shown in a high probability level accepted Ho hypothesis that the sequence does not exist autocorrelation.

(B) forecast

Conditional variance single step forward forecast average prediction error square and square root (RMSE), mean absolute error (MAE) and the average prediction error (MFE) the most commonly used indicator of three to measure the effect of time-series forecast measurements. FIGARCH model obtained for further testing of sample sequence portrayed effect, the same time, we established the sample sequence GARCH (concrete form omitted) and FIGARCH model comparison, predicted for sample 2006 19 to 29 April 10 days of data, and the results are shown in Table 5.

The results show the FIGARCH model GARCH models are less than the degree of deviation of the predicted values ??of the three indicators. This FIGARCH model conditional variance fluctuations predictive ability was significantly better than the GARCH model.

V. Conclusion

This article through the study found that the fluctuations in the Shanghai Stock Exchange Government Bond Index return series features the Shanghai Stock Exchange Government Bond Index yield not only has the general financial time series characteristics of non-normality and conditional heteroscedasticity, also has a long memory characteristics, whereby selected characterize time series is more suitable for long memory features FIGARCH (p, d, q) model on the Shanghai Stock Exchange Government Bond Index return series modeling.

Strong GARCH model predictive ability FIGARCH and Fractional model conditions on the Shanghai Stock Exchange bond index yield sequence variance fluctuations significantly. These conclusions are sure to provide a reference for the further deepening of China's bond market risk characteristics.

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