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Efficient inference in multivariate fractionally integrated time series models

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  • Morten Orregaard Nielsen

Abstract

We consider statistical inference for multivariate fractionally integrated time series models using a computationally simple conditional likelihood procedure which has recently been shown to be efficient in the univariate case. We show that those results generalize to the present multivariate setup, e.g. allowing us to efficiently estimate the memory parameters of vector ARFIMA models or test if two or more series are integrated of the same possibly fractional order. In particular, we show that all the desirable properties from standard statistical analysis apply for the time domain maximum likelihood estimator and related test statistics, i.e. consistency, standard asymptotic distributional properties, and under Gaussianity asymptotic efficiency. The finite sample properties of the likelihood ratio test are evaluated by Monte Carlo experiments, which show that rejection frequencies are very close to the asymptotic local power for samples as small as n=100.
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  • Morten Orregaard Nielsen, 2004. "Efficient inference in multivariate fractionally integrated time series models," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 63-97, June.
    • Handle: RePEc:ect:emjrnl:v:7:y:2004:i:1:p:63-97
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    1. Nielsen M.O., 2004. "Optimal Residual-Based Tests for Fractional Cointegration and Exchange Rate Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 331-345, July.
    2. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
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    6. Ling, Shiqing & Li, W.K., 2001. "Asymptotic Inference For Nonstationary Fractionally Integrated Autoregressive Moving-Average Models," Econometric Theory, Cambridge University Press, vol. 17(4), pages 738-764, August.
    7. Hosoya, Yuzo, 1996. "The quasi-likelihood approach to statistical inference on multiple time-series with long-range dependence," Journal of Econometrics, Elsevier, vol. 73(1), pages 217-236, July.
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    9. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
    10. Christos Agiakloglou & Paul Newbold, 1994. "Lagrange Multiplier Tests For Fractional Difference," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 253-262, May.
    11. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    12. Choi, In & Chul Ahn, Byung, 1998. "Testing the null of stationarity for multiple time series," Journal of Econometrics, Elsevier, vol. 88(1), pages 41-77, November.
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    Cited by:

    1. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    2. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.
    3. Daiqing Xi & Tianxiao Pang, 2021. "Estimating multiple breaks in mean sequentially with fractionally integrated errors," Statistical Papers, Springer, vol. 62(1), pages 451-494, February.
    4. Kristoufek, Ladislav, 2015. "On the interplay between short and long term memory in the power-law cross-correlations setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 218-222.
    5. P. S. Sephton, 2010. "Unit roots and purchasing power parity: another kick at the can," Applied Economics, Taylor & Francis Journals, vol. 42(27), pages 3439-3453.
    6. Marina Balboa & Paulo M. M. Rodrigues & Antonio Rubia & A. M. Robert Taylor, 2021. "Multivariate fractional integration tests allowing for conditional heteroskedasticity with an application to return volatility and trading volume," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 544-565, August.
    7. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    8. Tobias Hartl, 2020. "Macroeconomic Forecasting with Fractional Factor Models," Papers 2005.04897, arXiv.org.
    9. Mark J. Jensen, 2009. "The Long‐Run Fisher Effect: Can It Be Tested?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(1), pages 221-231, February.
    10. Hung Do & Rabindra Nepal & Russell Smyth, 2020. "Interconnectedness in the Australian National Electricity Market: A Higher‐Moment Analysis," The Economic Record, The Economic Society of Australia, vol. 96(315), pages 450-469, December.
    11. Fleming, Jeff & Kirby, Chris, 2011. "Long memory in volatility and trading volume," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1714-1726, July.
    12. Dark, Jonathan, 2018. "Multivariate models with long memory dependence in conditional correlation and volatility," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 162-180.
    13. Jorge M. L. Andraz & Raúl F. C. Guerreiro & Paulo M. M. Rodrigues, 2018. "Persistence of travel and leisure sector equity indices," Empirical Economics, Springer, vol. 54(4), pages 1801-1825, June.
    14. Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2013. "Fractionally Integrated VAR Models with a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-step Estimation," University of Regensburg Working Papers in Business, Economics and Management Information Systems 471, University of Regensburg, Department of Economics.
    15. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "A Multivariate Long-Memory Model with Structural Breaks," CESifo Working Paper Series 1950, CESifo.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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