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Non-stationary Gaussian ARFIMA processes: Estimation and application

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  • Lopes, Sílvia Regina Costa
  • Olbermann, Bárbara Patrícia
  • Reisen, Valderio Anselmo

Abstract

Recently, the study of time series turned the attention to the ones having long memory property. The ARFIMA (p,d,q) model shows this property when the degree of differencing d is in the interval (0.0,0.5), range where the process is stationary. In this work, we analyze the estimation of the degree d* in ARFIMA (p,d*,q) processes when d* >0.5, that is, when the processes are non-stationary but still have the property of long memory. We present a simulation study for the estimators of d* with semiparametric and parametric methods and different sample sizes. The methodology is applied to the experimental data series of UK long interest gilts.

Suggested Citation

  • Lopes, Sílvia Regina Costa & Olbermann, Bárbara Patrícia & Reisen, Valderio Anselmo, 2002. "Non-stationary Gaussian ARFIMA processes: Estimation and application," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 22(1), May.
    • Handle: RePEc:sbe:breart:v:22:y:2002:i:1:a:2746
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    2. Clifford M. Hurvich & Rohit S. Deo, 1999. "Plug‐in Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long‐memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(3), pages 331-341, May.
    3. Clifford M. Hurvich & Bonnie K. Ray, 1995. "Estimation Of The Memory Parameter For Nonstationary Or Noninvertible Fractionally Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 17-41, January.
    4. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    5. Liu, Ming, 1998. "Asymptotics Of Nonstationary Fractional Integrated Series," Econometric Theory, Cambridge University Press, vol. 14(5), pages 641-662, October.
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    Cited by:

    1. Salvatore Carta & Andrea Medda & Alessio Pili & Diego Reforgiato Recupero & Roberto Saia, 2018. "Forecasting E-Commerce Products Prices by Combining an Autoregressive Integrated Moving Average (ARIMA) Model and Google Trends Data," Future Internet, MDPI, vol. 11(1), pages 1-19, December.
    2. Irina Syssoyeva-Masson & João de Sousa Andrade, 2017. "The Effect of Public Debt on Growth in Multiple Regimes in the Presence of Long-Memory and Non-Stationary Debt Series," CeBER Working Papers 2017-07, Centre for Business and Economics Research (CeBER), University of Coimbra.
    3. Barbara Olbermann & Sílvia Lopes & Valdério Reisen, 2006. "Invariance of the first difference in ARFIMA models," Computational Statistics, Springer, vol. 21(3), pages 445-461, December.
    4. Joao Sousa Andrade & Irina Syssoyeva-Masson, 2016. "Investigating the presence of long memory in debt series and its relation with growth," EcoMod2016 9627, EcoMod.

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