Analyzing China’s Term Structure of Interest Rates Using VAR and Nelson-Siegel Model of

China’s bonds market has developed rapidly in recent years. A further study of interest rate term structure is essential. Nelson-Siegel model is widely used to fit interest rate term structure around the world. In this essay, we try to find out whether Nelson-Siegel model is efficiency in China, and which model is most efficient among some typical variants of Nelson-Siegel model. After brief theoretical introduction, we conduct empirical analysis, which contains two sections. In the first session, we focus on fitting Chinese interest rate term structure using Nelson-Siegel model, and fitting efficiency turns out to be pretty good. In the second section, we establish a VAR model with macroeconomic variables to predict parameters in Nelson-Siegel model, and use the combination of VAR and NS model to predict interest rate term structure in 2019 and 2020 respectively. Also, in terms of prediction efficiency, VAR (Macro)-NS model performs better than both VAR-NS model without macroeconomic variables and simple NS model. Term Interest

http://www.ccdc.com.cn/ccdc/en/index.shtml) as raw data, while other researchers usually use specific traded treasury bond in market. CCDC has already filtered market noise when CCDC calculates yield rate. Also, regulatory department has assigned CCDC's treasury bond yield curve as pricing benchmark. For example, China Banking Regulatory Commission requires commercial banks to use CCDC's treasury bond yield rate as benchmark of risk management. Second, based on trade experience in Chinese bond market, the paper introduced several typical macroeconomic variables into dynamic Nelson-Siegel model, and established VAR(Macro)-NS model. Third, in order to test the efficiency of VAR(Macro)-NS model, this paper introduces a VAR-NS model and a NS model. In addition, although there are already scholars around the world discussing the effect from macro variables on term structure, the importance of this topic is not highlighted in China, partly because of long-term regulated interest rate market and difficulty to get raw market data. This paper is first to fully exam effect from macro variables on term structure using most proper market data in

Literature Review
As scholars and investors use yield term structure more frequently, more relative models come up.
Nelson-Siegel model was first proposed by Nelson and Siegel (1987). This model is widely favored, for its intuitive economic explanation, less parameters to estimate and good fitting performance. However, Nelson-Siegel model fails to produce a multi-peak yield curve. Svensson (1994) added an exponential polynomial to solve the problem, and got Nelson-Siegel-Svensson model. Although Nelson-Siegel-Svensson model can generate a multi-peak yield curve, too many parameters makes it too sensitive to initial value.  [12], whose models with monetary policy variables significantly increased predictive ability during 2008 financial crisis.
Interest rate in China was partially regulated until recent years. As a result, Chinese scholar didn't pay much attention to macroeconomic variables and yield term structure before 2010. In recent years, relevant studies came up, as interest rate realized liberalization. Zeng and Niu (2013) became first Chinese scholar who got term structure of real interest rate and inflation rate, using no-arbitrage models. They also found that inflation rate affected more on short-term yields, while real interest rate affected more on long-term yields.
Qiang and Hou (2018) [13] built an affine interest rate model based on benchmark interest rate, market liquidity and risk premium, which explained the term structure well. They found that benchmark interest rate is determinant to other term yields, and market liquidity influence more on short-term yields, while risk premium affects more on long-term yields.

Brief Introduction to Nelson-Siegel Model
In 1987, Nelson and Siegel first use Nelson-Siegel model to fit yield curve, and the model is as follows.
Diebold and Li said that yield rate should change with time, and put forward Dynamic Nelson-Siegel model, and the model is as follows.
In the formula above, t represents a specific time point. τ represents time to maturity.
( ) t y τ represents the yield rate of a treasury bond with τ to maturity at time t. 1 2 3 , , t t t β β β and λ are parameters to be estimate.
• As τ approaches infinity, we get So 1t β is regarded as horizontal parameter. Change of 1t β will change the overall yield rate of a treasury bond.
• As τ approaches zero, we get • When τ is a normal number around 60, which means the treasury bond has 5 years (60 months) to maturity, we approximately get τ approaches infinity or zero, the third item approaches zero, which means its effect is around medium-term, as shown in Figure 2, so we can call it medium-term factor. So all factors that affect yield curve can be divided into these three group, as shown in Figure 3.

Can Nelson-Siegel Model Fit Chinese Treasury Bond Yield
Curve Well?

Search for Best Value of λ
Considering that λ has an influence on the fitting effect, we should first choose an optimal λ . Here we take this method. The first step is choose a certain λ , then we calculate 1 2 3 , , t t t β β β base on this given λ . After that, we use as our sample. Also, considering that bonds with more than 10 years to maturity may have deviation because of lack of liquidity, we choose bonds whose term to maturity is between 1 month and 10 years.
After all 65 trials, we find that, the estimation error is least when λ is 0.030, which means the medium factor become largest in around 4 th and 5 th year, as shown in Figure 4.

Test of Meaning of Parameters
As we discussed above, 1t β represents horizontal parameter, 2t β represents        β is correlated with IAV most, and 3t β is correlated with CPI most.

Variable Selection and Stationarity Test
The key to predict yield curve is to getting value of parameter 1 2 3 , , t t t β β β . We take VAR, or Vector Auto-regression Model, into consideration. As we discussed above, macroeconomics variables, including growth rate of Industry Added Value, CPI and M2, are closely related with parameter 1 2 3 , , t t t β β β . So, our model will include these macroeconomic variables.
The sample is monthly yield curve data from Jan 2002 to Dec 2018. We will use the model predict yield curve of 2019. Then we compare the predicted 2019 yield curve with observed yield curve.

Discussion on Prediction Result
After processing data, we get the result of VAR(macro)-NS model as follows.    Table 5.  Table 6 and Table 7.

Predict Yield Curve of 2020
Based  Table 8, Table 9 and Figure 8. 2) Yield curve 2020 is more flat than 2018 and 2019, which results from average 1,2020 β is smaller than 1,2018 β and 1,2019 β . A smaller 1,2020 β is the result of a lower growth rate of M2.

Conclusion
We settle down two main problems in the essay. First, we find that, although interest rate used to be incompletely regulated before 2014 in China, Nelson-Siegel model still shows excellent fitting efficiency. Second, we check whether adding