中国短期市场利率时间序列长记忆性实证研究
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摘要
近年来我国不少学者利用中国利率数据进行了短期市场利率时间序列的动态规律研究。从目前国内该领域的研究成果来看,大多数学者使用一些具有短期记忆特征的模型(如Vasicek、CIR和CKIS等模型)来刻画时间序列的动态规律,同时在研究中引入了条件异方差(ARCH族)、随机波动等模型来刻画利率变动的非正态性以及波动聚类效应等。
实证分析表明,金融市场上多数收益率的时间序列往往表现出明显的长期相关性,即长记忆性。短记忆性可以由传统的ARMA类模型来刻画,而长记忆性则可以利用分整过程I ( d )来描述,其中d是一个具体的实数。金融时间序列呈现出的尖峰肥尾的特征既可以由条件异方差性引起,也可以由长记忆过程引起。对于我国的市场利率时间序列而言,尖峰肥尾的特征同样普遍存在,但目前主要是用ARCH类模型来拟合。然而,我国短期市场利率是否也具有长记忆特征呢?如何建立能够同时捕捉长短记忆特性的动态模型?
本文较详细地阐述了长记忆时间序列及其各类模型,介绍了长记忆性的检验方法和模型估计,并以中国短期市场利率作为实证研究对象。我们对有代表性的7天期和14天期两种回购利率的时间序列进行了长记忆性的检验与比较,在此基础上通过一个ARFIMA-GARCH模型来刻画利率的长短记忆性,从而使我们进一步认识了利率市场的动态规律。
本文的创新之处有以下几个方面:1、对中国短期市场利率的动态行为首次采用长记忆时间序列模型进行研究;2、将得分检验法和ARFIMA模型估计相结合来检验判定序列是否具有长记忆性;3、使用改进的Hosking迭代法来估计ARFIMA -GARCH模型。
Instantaneous spot rates are key endogenous variables when we study the term structure of interest rates, and because of its basic affections on term structure of interest rates and modern finance, many people want to describe its dynamic change rules. However, we find short-term memory models (such as Vasicek、CIR and CKIS models) are used most frequently, in addition, we use such as conditional heteroscedastic models and stochastic volatility models to describe abnormal disturbance, and volatility clusters in interest rates.
Nowadays many people find there are always long period correlativity say, long-term memory, existed in time series of finance. We use such as ARMA models to describe short memory, as to long memory we use a fractional integrated process I ( d ) to do this job, here d is a real number. Excess kurtosis and fat tail characteristics in time series of interest rates indicates that the series is a nonlinear stochastic process which can be caused by conditional heteroscedastic( ARCH) or caused by long memory. While most studies on interest rates at home focused on the former. So our question is whether there is long memory in Chinese interest rates and how to describe it?
As many people in China used short memory models to study short market interest rate, in this article, we introduce long memory models of time series, ways to test long memory and model estimation. As short repo rates in China are quit representative of short market rates, we test and compared long and short term memories in 7-day and 14-day short repo rates, and using a ARFIMA -GARCHmodel to describe both long and short memories in interest rates.
The major contributions of this dissertation are: (1) first use long memory models to study time series of short market interest rates in China; (2) using score test together with estimateing ARFIMA model test long memory in time series; (3) estimate ARFIMA-GARCH model Hosking’s iteration method which has been improved by us.
实证分析表明,金融市场上多数收益率的时间序列往往表现出明显的长期相关性,即长记忆性。短记忆性可以由传统的ARMA类模型来刻画,而长记忆性则可以利用分整过程I ( d )来描述,其中d是一个具体的实数。金融时间序列呈现出的尖峰肥尾的特征既可以由条件异方差性引起,也可以由长记忆过程引起。对于我国的市场利率时间序列而言,尖峰肥尾的特征同样普遍存在,但目前主要是用ARCH类模型来拟合。然而,我国短期市场利率是否也具有长记忆特征呢?如何建立能够同时捕捉长短记忆特性的动态模型?
本文较详细地阐述了长记忆时间序列及其各类模型,介绍了长记忆性的检验方法和模型估计,并以中国短期市场利率作为实证研究对象。我们对有代表性的7天期和14天期两种回购利率的时间序列进行了长记忆性的检验与比较,在此基础上通过一个ARFIMA-GARCH模型来刻画利率的长短记忆性,从而使我们进一步认识了利率市场的动态规律。
本文的创新之处有以下几个方面:1、对中国短期市场利率的动态行为首次采用长记忆时间序列模型进行研究;2、将得分检验法和ARFIMA模型估计相结合来检验判定序列是否具有长记忆性;3、使用改进的Hosking迭代法来估计ARFIMA -GARCH模型。
Instantaneous spot rates are key endogenous variables when we study the term structure of interest rates, and because of its basic affections on term structure of interest rates and modern finance, many people want to describe its dynamic change rules. However, we find short-term memory models (such as Vasicek、CIR and CKIS models) are used most frequently, in addition, we use such as conditional heteroscedastic models and stochastic volatility models to describe abnormal disturbance, and volatility clusters in interest rates.
Nowadays many people find there are always long period correlativity say, long-term memory, existed in time series of finance. We use such as ARMA models to describe short memory, as to long memory we use a fractional integrated process I ( d ) to do this job, here d is a real number. Excess kurtosis and fat tail characteristics in time series of interest rates indicates that the series is a nonlinear stochastic process which can be caused by conditional heteroscedastic( ARCH) or caused by long memory. While most studies on interest rates at home focused on the former. So our question is whether there is long memory in Chinese interest rates and how to describe it?
As many people in China used short memory models to study short market interest rate, in this article, we introduce long memory models of time series, ways to test long memory and model estimation. As short repo rates in China are quit representative of short market rates, we test and compared long and short term memories in 7-day and 14-day short repo rates, and using a ARFIMA -GARCHmodel to describe both long and short memories in interest rates.
The major contributions of this dissertation are: (1) first use long memory models to study time series of short market interest rates in China; (2) using score test together with estimateing ARFIMA model test long memory in time series; (3) estimate ARFIMA-GARCH model Hosking’s iteration method which has been improved by us.
引文
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[2] Anderson, T.G. and J. Lund, 1997. Estimating Continuous-Time Stochastic Volatility Models of the Short- Term Interest Rate【J】Journal of Econometrics 72, 343-377
[3] ARTECHE, J. (2002) Semiparametric Robust Tests on Seasonal or Cyclical Long Memory TimeSeries. Journal of Time Series Analysis, 23(3): 251-285
[4] ARTECHE, J., P. M. ROBINSON (2000) Semiparametric Inference in Seasonal and CyclicalLong Memory Processes. Journal of Time Series Analysis, 21(1): 1-25
[5] Backus, D.&Zin, S.,1993. Long memory inflation uncertainty: Evidence of term structure of interest rate.【J】 Journal of Money, Credit and Banking, 25, 687–700
[6] BAILLIE, R. T., T. BOLLERSLEV, H. O. MIKKELSEN. 1996. Fractionally integrated generalized autoregressive conditional heteroskedasticity【J】 Journal of Econometrics, 74: 3-30.
[7] BAILLIE, R. T., C.-F. CHUNG, M. A. TIESLAU 1996. Analysing inflation by the Fractionally Integrated Arfima-Garch Model【J】 Journal of applied Econometrics, 11(1): 23-40.
[8] Baillie, R. T.1996. Long Memory Processes and Fractional Integration in Econometrics 【J】Journal of Econometrics, 73, 5-59
[9] Baz, J. and S.R. Das .1996. Analytical Approximation of the Term Structure for Jump-Diffusion Process: a Numerical Analysis【J】Journal of Fixed Income 6, 78-86.
[10] Beran, J. 1995. Maximum likelihood estimation of differencing parameter for invertible short and long memory autoregressive integrated moving average models【J】 Journal of the Royal Statistical Society, Series B. 57(4): 659-672
[11] BOLLERSLEV, T., H. O. MIKKELSEN. 1996. Modeling and pricing long memory in stock market volatility【J】 Journal of Econometrics, 73: 151-184.
[12] BREIDT, F. J., N. CRATO, P. de LIMA. 1998. The detection and estimation of long memory in stochastic volatility【J】 Journal of Econometrics, 83: 325-348.
[13] Brock, W. A., Dechert, W. D., and Scheinkman, J. A.1987. A Test for Independence based on Correlation Dimension 【J】 unpublished manuscript
[14] Brockwell, P, J.,R.A.Davis.1991. Time series: Theory and Methods【M】 Springer-Verlag
[15] Chan, K. C., G. A.Karolyi, F.A.Longstaff and A.B.Sanders 1992. An Empirical Comparison of Alternative Models of the Short-Term Interest Rate【J】 Journal of Finance, 47,1209-1227.
[16] CHEUNG, Y.-W. 1993. Long memory in foreign exchange rates【J】 Journal of Business and Economic Statistics, 11: 93-101.
[17] COMTE, F., E. RENAULT. 1996. Long memory continuous time model【sJ】 Journal of Econometrics, 73: 101-149.
[18] Connolly, R., & Guner, N. 1999. Long memory characteristics of the distributions of treasury security yields, returns and volatility (Working Paper) 【J】Chapel Hill: University of North Carolina
[19] Cox, J. C., J. E. Ingersoll and S. A. Ross 1985. A Theory of the Term Structure of Interest Rates【J】 Econometrica 53, 385-407.
[20] Dai, Q. and K. Singleton. 2003. Term Structure Dynamics in Theory and Reality【J】 Review of Financial Studies 16, 631-678.
[21] Das, S. R. 2002. The Surprise Element: Jumps in Interest Rates【J】Journal of Econometrics 106, 27-65.
[22] DING, Z., C. W. J. GRANGER, R. ENGLE. 1993. A long memory property of stock market returns and a new model【J】 Journal of Empirical Finance, 1:83-106.
[23] DING, Z., C. W. J. GRANGER. 1996. Modelling volatility persistence of speculative returns: A new approach【J】 Journal of Econometrics, 73: 185-215.
[24] Edgar E. Peters著 储海林 殷勤译《分行市场分析-将混沌理论应用到投资与经济理论上》【M】22,60,72,103 经济科学出版社 北京 2002
[25] Edgar E. Peters著 王小东译《资本市场的混沌与秩序》(第二版)【M】经济科学出版社 北京 1999
[26] Edgar, E. P. 1991. Chaos and Order in the Capital Markets【M】Wiley, New York
[27] Gallant, A. R. and G. Tauchen 1998. Reprojection Partially Observed Systems With Applications to Interest Rate Diffusions【J】 Journal of the American Statistical Association 93, 10-24.
[28] Geweke,J. and S. Porter-Hudak 1983 The estimation and application of long memory time series models【J】 Journal of Time Series Analysis 4, 221-238
[29] Granger, C. W. J. 1980. Long memory relationships and the aggregation of dynamic models 【J】Journal of Econometrics, 14, 227-238
[30] Granger, C. W. J., Zhuanxin Ding. 1996. Varieties of long memory models 【J】 Journal of Econometrics 73, 61-78
[31] Granger,C.W.J. and R.Joyeux. 1980. An introduction to long memory time seires models and fractional differencing【J】 Journal of Time Series Analysis 1, 5-39
[32] Gray, H. L., Nien-Fan Zhang, Woodward, W. A. 1989. One generalized fractional processes【J】 Journal of Time Series Analysis 10(3): 233-257
[33] Hong, Y. and H. Li. 2004. Nonparametric Specification Testing for Continuous-Time Models With Applications to Interest Rate Term Structuresv【J】 Review of Financial Studies, forthcoming.
[34] Horst, H. E. 1951. Long-term storage capacity of reservoirs 【J】Transactions of the American Society of Civil Engineers 116, 770-779
[35] Hosking, J. R. M. 1981. Fractional differencing 【J】Biometrika 68, 165-176
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