Dechert, Andreas (2012): Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks.
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Modeling fractional cointegration relationships has become a major topic in applied time series analysis as it steps back from the traditional rigid I(1)/I(0) methodology. Hence, the number of proposed tests and approaches has grown over the last decade. The aim of this paper is to study the nonparametric variance ratio approach suggested by Nielsen for the case of fractional cointegration in presence of linear trend and trend breaks. The consideration of trend breaks is very important in order to avoid spurious fractional integration, so this possibility should be regarded by practitioners. This paper proposes to calculate p-values by means of gamma distributions and gives response regressions parameters for the asymptotic moments of them. In Monte Carlo simulations this work compares the power of the approach against a Johansen type rank test suggested, which is robust against trend breaks but not fractional (co-)integration. As the approach also obtains an estimator for the cointegration space, the paper compares it with OLS estimates in simulations. As an empirical example the validity of the market expectation hypothesis is tested for monthly Treasury bill rates ranging from 1958-2011, which might have a trend break around September 1979 due to change of American monetary policy.
|Item Type:||MPRA Paper|
|Original Title:||Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks|
|Keywords:||fractional integration; fractional cointegration; long memory; variance ratio; nonparametric; trend breaks; market expectation hypothesis|
|Subjects:||C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models; Multiple Variables > C32 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General
|Depositing User:||Andreas Dechert|
|Date Deposited:||05. Sep 2012 14:04|
|Last Modified:||11. Feb 2013 18:20|
Breitung, J., Hassler, U. (2002): Inference on the cointegration rank in fractionally integrated processes. Journal of Econometrics 110, 167-185.
Campbell, J. Y., Shiller, R. J. (1987): Cointegration and tests of present value models. Journal of Political Economy 95, 1062-1088.
Doornik, J. A. (1998): Approximations to the Asymptotic Distribution of Cointegration Tests. Journal of Economic Surveys 12, 573-593.
Engle, R. F., Granger, C. W. J. (1987): Co-Integration and error correction: Representation, estimation and testing. Econometrica 55, 251-276.
Engsted, T., Tanggaard, C. (1994): Cointegration and the US term structure. Journal of Banking and Finance 18, 167-181.
Hall, A. D., Anderson, H. M., Granger C. W. J. (1992): A cointegration analysis of treasury bill yields. Review of Economics and Statistics 74, 116-126.
Hosking, J. R. M. (1980): Fractional differencing. Biometrika 68, 165-176.
Iacone, F. (2009): A semiparametric analysis of the term structure of the US interest rates. Oxford Bulletin of Economics and Statistics 71, 475-490.
Johansen, S., Mosconi, R., Nielsen, B. (2000): Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal 3, 216-249.
Johansen, S. (2008): A representation theory for a class of vector autoregressive models for fractional processes. Econometric Theory 24, 651-676.
Johansen, S., Nielsen, M. Ø. (2011): Likelihood inference for a fractionally cointegrated vector autoregressive model. Working Paper.
Marinucci, D., Robinson, P. M. (1999): Alternative forms of fractional Brownian Motion. Journal of Statistical Planing and Inference 80, 111-122.
Nielsen, M. Ø., Shimotsu, K. (2007): Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach. Journal of Econometrics 141, 574-596.
Nielsen, M. Ø. (2008): A powerful test of the autoregressive unit root hypothesis based on a tuning parameter free statistic. Econometric Theory 25, 1515-1544.
Nielsen, M. Ø. (2010): Nonparametric cointegration analysis of fractional systems with unknown integration orders. Journal of Econometrics 155, 170-187.
Perron, P. (1989): The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57, 1361-1401.
Phillips, P. C. B., Ouliaris, S. (1988): Testing for cointegration using principal components methods. Journal of Economic Dynamics and Control 12, 205-230.
Robinson, P. M. (1995): Gaussian semiparametric estimation of long range dependence. Annals of Statistics 23, 1630-1661.
Robinson, P. M., Yajima, Y. (2002): Determination of cointegrating rank in fractional systems. Journal of Econometrics 106, 217-241.
Shimotsu, K., Phillips, P.C.B (2006): Local Whittle estimation of fractional integration and some of its variants. Journal of Econometrics 130, 209-333.
Shimotsu, K. (2010): Exact local Whittle estimation of fractional integration with unknown mean and time trend. Econometric Theory 26, 501-540.