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Infinite Variance Stable Arma Processes

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  • Piotr S. Kokoszka
  • Murad S. Taqqu

Abstract

. The asymptotic dependence structure of autoregressive moving‐average processes with stable innovations is analyzed. The analysis is carried out by means of a measure of dependence which extends the covariance function and is applicable to stochastic processes with infinite variance.

Suggested Citation

  • Piotr S. Kokoszka & Murad S. Taqqu, 1994. "Infinite Variance Stable Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 203-220, March.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:2:p:203-220
    DOI: 10.1111/j.1467-9892.1994.tb00185.x
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    Citations

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    Cited by:

    1. Rosadi, Dedi, 2009. "Testing for independence in heavy-tailed time series using the codifference function," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4516-4529, October.
    2. Damarackas, Julius & Paulauskas, Vygantas, 2017. "Spectral covariance and limit theorems for random fields with infinite variance," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 156-175.
    3. Jonathan B. Hill, 2004. "Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Time Series with an Application," Econometrics 0411014, University Library of Munich, Germany, revised 04 Nov 2005.
    4. Karling, Maicon J. & Lopes, Sílvia R.C. & de Souza, Roberto M., 2023. "Multivariate α-stable distributions: VAR(1) processes, measures of dependence and their estimations," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    5. Kokoszka, Piotr S. & Taqqu, Murad S., 1996. "Infinite variance stable moving averages with long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 79-99, July.
    6. Sampaio, Jhames M. & Morettin, Pedro A., 2020. "Stable Randomized Generalized Autoregressive Conditional Heteroskedastic Models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 67-83.
    7. Marco J. Lombardi & Giorgio Calzolari, 2008. "Indirect Estimation of α-Stable Distributions and Processes," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 193-208, March.
    8. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
    9. Dedi Rosadi & Manfred Deistler, 2011. "Estimating the codifference function of linear time series models with infinite variance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 395-429, May.
    10. Piotr Kokoszka & Michael Wolf, 2004. "Subsampling the mean of heavy‐tailed dependent observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 217-234, March.

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