On the Identification of Fractionally Cointegrated VAR Models With the F(d) Condition

References

• Avarucci, M., and Velasco, C. (2009), “A Wald Test for the Cointegration Rank in Nonstationary Fractional Systems,” Journal of Econometrics, 151, 178–189.
   Web of Science ®Google Scholar
• Bollerslev, T., Osterrieder, D., Sizova, N., and Tauchen, G. (2013), “Risk and Return: Long-Run Relations, Fractional Cointegration, and Return Predictability,” Journal of Financial Economics, 108, 409–424.
   Web of Science ®Google Scholar
• Breitung, J., and Hassler, U. (2002), “Inference on the Cointegration Rank in Fractionally Integrated Processes,” Journal of Econometrics, 110, 167–185.
   Web of Science ®Google Scholar
• Caporin, M., Ranaldo, A., and Santucci de Magistris, P. (2013), “On the Predictability of Stock Prices: A Case for High and Low Prices,” Journal of Banking & Finance, 37, 5132–5146.
   Web of Science ®Google Scholar
• Chen, W., and Hurvich, C. (2003), “Semiparametric Estimation of Multivariate Fractional Cointegration,” Journal of the American Statistical Association, 98, 629–642.
   Web of Science ®Google Scholar
• ——— (2006), “Semiparametric Estimation of Fractional Cointegrating Subspaces,” Annals of Statistics, 34, 2939–2979.
   Web of Science ®Google Scholar
• Christensen, B. J., and Nielsen, M. Ø. (2006), “Asymptotic Normality of Narrow-Band Least Squares in the Stationary Fractional Cointegration Model and Volatility Forecasting,” Journal of Econometrics, 133, 343–371.
   Web of Science ®Google Scholar
• Franchi, M. (2010), “A Representation Theory for Polynomial Cofractionality in Vector Autoregressive Models,” Econometric Theory, 26, 1201–1217.
   Web of Science ®Google Scholar
• Granger, C. W. J. (1986), “Developments in the Study of Cointegrated Economic Variables,” Oxford Bulletin of Economics and Statistics, 48, 213–28.
   Web of Science ®Google Scholar
• Hualde, J., and Velasco, C. (2008), “Distribution-Free Tests of Fractional Cointegration,” Econometric Theory, 24, 216–255.
   Web of Science ®Google Scholar
• Johansen, S. (1988), “Statistical Analysis of Cointegration Vectors,” Journal of Economic Dynamics and Control, 12, 231–254.
   Web of Science ®Google Scholar
• ——— (1995a), Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford: Oxford University Press.
   Google Scholar
• ——— (1995b), “A Stastistical Analysis of Cointegration for I(2) Variables,” Econometric Theory, 11, 25–59.
   Web of Science ®Google Scholar
• ——— (2008), “A Representation Theory for a Class of Vector Autoregressive Models for Fractional Processes,” Econometric Theory, 24, 651–676.
   Web of Science ®Google Scholar
• ——— (2010), “Some Identification Problems in the Cointegrated Vector Autoregressive Model,” Journal of Econometrics, 158, 262–273.
   Web of Science ®Google Scholar
• Johansen, S., and Nielsen, M. Ø. (2010), “Likelihood Inference for a Nonstationary Fractional Autoregressive Model,” Journal of Econometrics, 158, 51–66.
   Web of Science ®Google Scholar
• ——— (2012), “Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model,” Econometrica, 80, 2667–2732.
   Web of Science ®Google Scholar
• Łasak, K. (2010), “Likelihood Based Testing for No Fractional Cointegration,” Journal of Econometrics, 158, 67–77.
   Web of Science ®Google Scholar
• Łasak, K., and Velasco, C. (2015), “Fractional Cointegration Rank Estimation,” Journal of Business & Economic Statistics, 33, 241–254.
   Web of Science ®Google Scholar
• MacKinnon, J. G., and Nielsen, M. Ø. (2014), “Numerical Distribution Functions Of Fractional Unit Root And Cointegration Tests,” Journal of Applied Econometrics, 29, 161–171.
   Web of Science ®Google Scholar
• Nielsen, B. (2006), Order Determination in General Vector Autoregressions, Volume 52 of Lecture Notes–Monograph Series, Hayward, CA: Institute of Mathematical Statistics, pp. 93–112.
   Google Scholar
• Nielsen, M. Ø. and Popiel, M. K. (2016), “A MATLAB Program and User’s Guide for the Fractionally Cointegrated VAR Model,” Working Paper, Queen’s University.
   Google Scholar
• Nielsen, M. Ø. and Shimotsu, K. (2007), “Determining the Cointegration Rank in Nonstationary Fractional System by the Exact Local Whittle Approach,” Journal of Econometrics, 141, 574–596.
   Web of Science ®Google Scholar
• Robinson, P. M., and Marinucci, D. (2003), “Semiparametric Frequency Domain Analysis of Fractional Cointegration,” in Time Series with Long Memory, ed. P. M. Robinson, Oxford University Press, pp. 334–373.
   Google Scholar
• Robinson, P. M., and Yajima, Y. (2002), “Determination of Cointegrating Rank in Fractional Systems,” Journal of Econometrics, 106, 217–241.
   Web of Science ®Google Scholar
• Shimotsu, K., and Phillips, P. C. (2005), “Exact Local Whittle Estimation of Fractional Integration,” Annals of Statistics, 33, 1890–1933.
   Web of Science ®Google Scholar
• Tschernig, R., Weber, E., and Weigand, R. (2013a), “Fractionally Integrated VAR Models With a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-Step Estimation,” Working Paper, University of Regensburg.
   Google Scholar
• ——— (2013b), “Long-Run Identification in a Fractionally Integrated System,” Journal of Business & Economic Statistics, 31, 438–450.
   Web of Science ®Google Scholar