Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/aah/create/2011-14.html
   My bibliography  Save this paper

When Long Memory Meets the Kalman Filter: A Comparative Study

Author

Listed:
  • Stefano Grassi

    (Aarhus University and CREATES)

  • Paolo Santucci de Magistris

    (Aarhus University and CREATES)

Abstract
The finite sample properties of the state space methods applied to long memory time series are analyzed through Monte Carlo simulations. The state space setup allows to introduce a novel modeling approach in the long memory framework, which directly tackles measurement errors and random level shifts. Missing values and several alternative sources of misspecification are also considered. It emerges that the state space methodology provides a valuable alternative for the estimation of the long memory models, under different data generating processes, which are common in financial and economic series. Two empirical applications highlight the practical usefulness of the proposed state space methods.

Suggested Citation

  • Stefano Grassi & Paolo Santucci de Magistris, 2011. "When Long Memory Meets the Kalman Filter: A Comparative Study," CREATES Research Papers 2011-14, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2011-14
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/11/rp11_14.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Diebold, Francis X & Husted, Steven & Rush, Mark, 1991. "Real Exchange Rates under the Gold Standard," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1252-1271, December.
    2. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    3. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    4. Bisaglia, Luisa & Guegan, Dominique, 1998. "A comparison of techniques of estimation in long-memory processes," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 61-81, March.
    5. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    6. Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation Of Fractional Integration With Unknown Mean And Time Trend," Econometric Theory, Cambridge University Press, vol. 26(2), pages 501-540, April.
    7. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    8. Harvey, Andrew & Proietti, Tommaso (ed.), 2005. "Readings in Unobserved Components Models," OUP Catalogue, Oxford University Press, number 9780199278695.
    9. Qu, Zhongjun, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 423-438.
    10. Ohanissian, Arek & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "True or Spurious Long Memory? A New Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 161-175, April.
    11. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    12. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
    13. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    14. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    15. María Dolores Gadea & Laura Mayoral, 2006. "The Persistence of Inflation in OECD Countries: A Fractionally Integrated Approach," International Journal of Central Banking, International Journal of Central Banking, vol. 2(1), March.
    16. Philipp Sibbertsen & Robinson Kruse, 2009. "Testing for a break in persistence under long‐range dependencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 263-285, May.
    17. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
    18. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    19. Iglesias, Pilar & Jorquera, Hector & Palma, Wilfredo, 2006. "Data analysis using regression models with missing observations and long-memory: an application study," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2028-2043, April.
    20. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, July.
    21. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 138-156, January.
    22. Haldrup, Niels & Nielsen, Morten Orregaard, 2007. "Estimation of fractional integration in the presence of data noise," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3100-3114, March.
    23. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(4), pages 686-710, August.
    24. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    25. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    26. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    27. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    28. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    29. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
    30. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    31. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "What is What? A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Working Papers 258, Barcelona School of Economics.
    32. Pipiras, Vladas & Taqqu, Murad S. & Abry, Patrice, 2003. "Can continuous-time stationary stable processes have discrete linear representations?," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 147-157, August.
    33. Clifford M. Hurvich & Bonnie K. Ray, 2003. "The Local Whittle Estimator of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 1(3), pages 445-470.
    34. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    35. Baillie, Richard T & Chung, Ching-Fan & Tieslau, Margie A, 1996. "Analysing Inflation by the Fractionally Integrated ARFIMA-GARCH Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 23-40, Jan.-Feb..
    36. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    37. Luisa Bisaglia & Dominique Guegan, 1998. "A comparison of techniques of estimation in long-memory processes," Post-Print halshs-00194462, HAL.
    38. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
    39. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    40. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rasmus T. Varneskov & Pierre Perron, 2018. "Combining long memory and level shifts in modelling and forecasting the volatility of asset returns," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 371-393, March.
    2. Claudio Morana, 2014. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks," Working Papers 273, University of Milano-Bicocca, Department of Economics, revised May 2014.
    3. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 2015. "Testing for Level Shifts in Fractionally Integrated Processes: a State Space Approach," CREATES Research Papers 2015-30, Department of Economics and Business Economics, Aarhus University.
    4. Andersson, Fredrik N.G. & Li, Yushu, 2013. "How Flexible are the Inflation Targets? A Bayesian MCMC Estimator of the Long Memory Parameter in a State Space Model," Working Papers 2013:38, Lund University, Department of Economics.
    5. Cuestas Juan Carlos & Gil-Alana Luis Alberiko, 2016. "Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(1), pages 57-74, February.
    6. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 2017. "Does the ARFIMA really shift?," CREATES Research Papers 2017-16, Department of Economics and Business Economics, Aarhus University.
    7. Salman Huseynov, 2021. "Long and short memory in dynamic term structure models," CREATES Research Papers 2021-15, Department of Economics and Business Economics, Aarhus University.
    8. Kruse, Robinson, 2015. "A modified test against spurious long memory," Economics Letters, Elsevier, vol. 135(C), pages 34-38.
    9. Andersson, Fredrik N. G. & Li, Yushu, 2014. "Are Central Bankers Inflation Nutters? - A Bayesian MCMC Estimator of the Long Memory Parameter in a State Space Model," Discussion Papers 2014/38, Norwegian School of Economics, Department of Business and Management Science.
    10. 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.
    11. Dissanayake, G.S. & Peiris, M.S. & Proietti, T., 2016. "State space modeling of Gegenbauer processes with long memory," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 115-130.
    12. Fredrik N. G. Andersson & Yushu Li, 2020. "Are Central Bankers Inflation Nutters? An MCMC Estimator of the Long-Memory Parameter in a State Space Model," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 529-549, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    2. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 2017. "Does the ARFIMA really shift?," CREATES Research Papers 2017-16, Department of Economics and Business Economics, Aarhus University.
    3. Davide Delle Monache & Stefano Grassi & Paolo Santucci, 2015. "Testing for Level Shifts in Fractionally Integrated Processes: a State Space Approach," Studies in Economics 1511, School of Economics, University of Kent.
    4. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    5. Christensen, Bent Jesper & Varneskov, Rasmus Tangsgaard, 2017. "Medium band least squares estimation of fractional cointegration in the presence of low-frequency contamination," Journal of Econometrics, Elsevier, vol. 197(2), pages 218-244.
    6. Hou, Jie & Perron, Pierre, 2014. "Modified local Whittle estimator for long memory processes in the presence of low frequency (and other) contaminations," Journal of Econometrics, Elsevier, vol. 182(2), pages 309-328.
    7. Abderrazak Ben Maatoug & Rim Lamouchi & Russell Davidson & Ibrahim Fatnassi, 2018. "Modelling Foreign Exchange Realized Volatility Using High Frequency Data: Long Memory versus Structural Breaks," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 10(1), pages 1-25, March.
    8. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1196-1237, December.
    9. Ata Assaf & Luis Alberiko Gil-Alana & Khaled Mokni, 2022. "True or spurious long memory in the cryptocurrency markets: evidence from a multivariate test and other Whittle estimation methods," Empirical Economics, Springer, vol. 63(3), pages 1543-1570, September.
    10. Giorgio Canarella & Stephen M. Miller, 2016. "Inflation Persistence and Structural Breaks: The Experience of Inflation Targeting Countries and the US," Working papers 2016-11, University of Connecticut, Department of Economics.
    11. Arturo Leccadito & Omar Rachedi & Giovanni Urga, 2015. "True Versus Spurious Long Memory: Some Theoretical Results and a Monte Carlo Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 34(4), pages 452-479, April.
    12. Marie Busch & Philipp Sibbertsen, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Econometrics, MDPI, vol. 6(1), pages 1-21, March.
    13. Renzo Pardo Figueroa & Gabriel Rodríguez, 2014. "Distinguishing between True and Spurious Long Memory in the Volatility of Stock Market Returns in Latin America," Documentos de Trabajo / Working Papers 2014-395, Departamento de Economía - Pontificia Universidad Católica del Perú.
    14. Canarella, Giorgio & Miller, Stephen M., 2017. "Inflation targeting and inflation persistence: New evidence from fractional integration and cointegration," Journal of Economics and Business, Elsevier, vol. 92(C), pages 45-62.
    15. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, Department of Economics and Business Economics, Aarhus University.
    16. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2017. "The Memory of Volatility," Hannover Economic Papers (HEP) dp-601, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    17. Frederiksen, Per & Nielsen, Frank S. & Nielsen, Morten Ørregaard, 2012. "Local polynomial Whittle estimation of perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 167(2), pages 426-447.
    18. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    19. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    20. Isao Ishida & Toshiaki Watanabe, 2009. "Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model," CARF F-Series CARF-F-145, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    More about this item

    Keywords

    ARFIMA models; Kalman Filter; Missing Observations; Measurement Error; Level Shifts.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aah:create:2011-14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.