条件异方差动态Nelson-Siegel利率期限结构模型及其应用

Dynamic Nelson-Siegel Term Structure Model with GARCH Error Terms and It’s Applications

动态Nelson-Siegel(DNS)利率期限结构模型将方差设定为常数,不能刻画收益率序列的条件异方差,降低了数据拟合和预测能力。本文用GARCH模型设定DNS模型观测方程条件异方差,基于适应状态空间模型用广义自回归得分(GAS)设定转移方程条件异方差矩阵,提出具有时变方差的GAS-DNS模型,将Rapisarda等的矩阵分解方法应用于协方差矩阵分解及再参数化保证协方差矩阵的正定性。采用中国银行间市场13种期限国债收益率数据进行实证分析,极大似然比检验表明,将DNS模型误差项方差矩阵时变化能够显著提高模型的对数似然值;以MAE、RMSE、MAPE和TIC为标准进行比较,显示GAS-DNS模型的收益率曲线样本内拟合效果和样本外预测能力均比DNS模型有显著提高。本文提出的GAS-DNS模型是对DNS模型的实质改进,鉴于利率期限结构模型和利率预测在实际应用中的重要性,本文的模型改进具有应用价值。

Dynamic Nelson-Siegel term structure model(DNS hereafter)of interest rate has been extensively studied and widely applied because of its strong ability to fit yield curve.The DNS model has been reformulated as a linear Gaussian state space model with error terms of constant variances both in measurement and transition equations,which is not able to capture the dynamics in conditional covariance of yields.In this article,the conditional heteroscedasticity in the error terms of the DNS model is introduced to improve its fitting performance and forecasting ability.We extend the model by specifying the dynamic models of error term variances in measurement equation as GARCH and that in transition equation as general autoregressive score(GAS)proposed by Creal et al.(2013)using observation-driven method.The decomposition and reparameterization methods are employed to ensure the positiveness of conditional variance matrix.The empirical evidence of considerable increase in within-sample fitting and out-of-sample forecasting goodness for these advances is present in the dynamic Nelson-Siegel model in China bond market.