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Combining Long and Short Memory in Time Series Models: the Role of Asymptotic Correlations of the MLEs

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  • Baillie, Richard T.
  • Cho, Dooyeon
  • Rho, Seunghwa

Abstract

A major practical problem in the application of the long memory ARFIMA model has been distinguishing between the long memory and short memory components and subsequent estimation of the model. The asymptotic correlations between the Maximum Likelihood Estimators (MLE) of the long memory parameter, d, and the short memory parameters within an ARFIMA estimation are derived. The correlation in an ARFIMA(1,d,0) model can be as large as −0.95. However, MLE still works well in these high correlation cases; even for non stationary situations. Similarly, QMLE also performs well in simulations where the innovations have t or skewed t densities. MLE also performs very well for ARFIMA(3,d,0) models when there is a moderate level of persistence in the short memory part. However, MLE can perform extremely poorly when there is a combination of long memory and substantial persistence in the short memory component. Some of these points are illustrated in the analysis of some Realized Volatility time series which contain long memory. The correlation in “gap ARFIMA” models is comparatively low which indicates that MLE is quite stable in this case. Some suggestions and recommendations for applied work are provided.

Suggested Citation

  • Baillie, Richard T. & Cho, Dooyeon & Rho, Seunghwa, 2024. "Combining Long and Short Memory in Time Series Models: the Role of Asymptotic Correlations of the MLEs," Econometrics and Statistics, Elsevier, vol. 29(C), pages 88-112.
    • Handle: RePEc:eee:ecosta:v:29:y:2024:i:c:p:88-112
    DOI: 10.1016/j.ecosta.2022.06.001
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    References listed on IDEAS

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    1. Jack H. W. Penm & R. D. Terrell, 1982. "On The Recursive Fitting Of Subset Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(1), pages 43-59, January.
    2. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    3. Baillie, Richard T. & Kapetanios, George, 2008. "Nonlinear models for strongly dependent processes with financial applications," Journal of Econometrics, Elsevier, vol. 147(1), pages 60-71, November.
    4. Baillie, Richard T. & Morana, Claudio, 2012. "Adaptive ARFIMA models with applications to inflation," Economic Modelling, Elsevier, vol. 29(6), pages 2451-2459.
    5. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, vol. 45(4), pages 465-515, October.
    6. Leschinski, Christian & Sibbertsen, Philipp, 2019. "Model order selection in periodic long memory models," Econometrics and Statistics, Elsevier, vol. 9(C), pages 78-94.
    7. Philip Hans Franses & Marius Ooms & Charles S. Bos, 1999. "Long memory and level shifts: Re-analyzing inflation rates," Empirical Economics, Springer, vol. 24(3), pages 427-449.
    8. Andreas Noack Jensen & Morten Ørregaard Nielsen, 2014. "A Fast Fractional Difference Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 428-436, August.
    9. Richard T. Baillie & George Kapetanios, 2013. "Estimation and inference for impulse response functions from univariate strongly persistent processes," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 373-399, October.
    10. 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..
    11. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    12. Penm, J. H. W. & Terrell, R. D., 1984. "Multivariate subset autoregressive modelling with zero constraints for detecting 'overall causality'," Journal of Econometrics, Elsevier, vol. 24(3), pages 311-330, March.
    13. Richard T. Baillie & Fabio Calonaci & Dooyeon Cho & Seunghwa Rho, 2019. "Long Memory, Realized Volatility and Heterogeneous Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(4), pages 609-628, July.
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    More about this item

    Keywords

    Long memory; ARFIMA; Strong persistence in short memory; Correlations between MLEs of parameters;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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