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Stochastic Orders Of Magnitude Associated With Two‐Stage Estimators Of Fractional Arima Systems

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  • J. H. Wright

Abstract

. Two‐stage estimators have been proposed in fractional autoregressive integrated moving‐average (ARIMA) systems which first estimate the long‐run features of the system semi‐parametrically and then estimate the short‐run features by usual methods in a second stage. Although asymptotic theory is available for the estimates in the first stage of such a procedure, we are aware of no results concerning the estimates in the second stage. In this paper we provide a stochastic order of magnitude associated with an estimator in this class and discuss this result.

Suggested Citation

  • J. H. Wright, 1995. "Stochastic Orders Of Magnitude Associated With Two‐Stage Estimators Of Fractional Arima Systems," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 119-125, January.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:1:p:119-125
    DOI: 10.1111/j.1467-9892.1995.tb00225.x
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    1. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    2. G. J. Janacek, 1982. "Determining The Degree Of Differencing For Time Series Via The Log Spectrum," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 177-183, May.
    3. 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.
    4. P. M. Robinson, 1987. "Time Series Residuals With Application To Probability Density Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 329-344, May.
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