IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v36y2015i6p853-875.html
   My bibliography  Save this article

Mixed-Norm Spaces and Prediction of SαS Moving Averages

Author

Listed:
  • Raymond Cheng
  • Charles B. Harris

Abstract

type="main" xml:id="jtsa12134-abs-0001"> Suppose that Z k k = − ∞ ∞ is an i.i.d. symmetric α-stable noise, 1 > α > 2, and consider the moving average process X k k = − ∞ ∞ given by X k = ∑ j = 0 ∞ a j Z k − j . Conditions are obtained for the convergence rate of the moving average series, as well as that of the inverted (autoregressive) representation Z k = ∑ j = 0 ∞ c j X k − j . These conditions are expressed in terms of the associated function F ( z ) = ∑ j = 0 ∞ a j z j and its reciprocal belonging to certain mixed-norm spaces of functions on the open unit disc. Properties of these spaces are explored. Criteria are also derived for the rate of mixing in a certain sense.

Suggested Citation

  • Raymond Cheng & Charles B. Harris, 2015. "Mixed-Norm Spaces and Prediction of SαS Moving Averages," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 853-875, November.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:6:p:853-875
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/jtsa.12134
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Cheng, R., 1992. "Hölder classes of vector-valued functions and convergence of the best predictor," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 110-129, July.
    3. Pourahmadi, Mohsen, 1989. "On the convergence of finite linear predictors of stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 167-180, August.
    4. Levy, Joshua B. & Taqqu, Murad S., 2014. "The asymptotic codifference and covariation of log-fractional stable noise," Journal of Econometrics, Elsevier, vol. 181(1), pages 34-43.
    5. Doukhan, Paul & Fokianos, Konstantinos & Li, Xiaoyin, 2012. "On weak dependence conditions: The case of discrete valued processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1941-1948.
    Full references (including those not matched with items on IDEAS)

    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. Boris Aleksandrov & Christian H. Weiß & Carsten Jentsch, 2022. "Goodness‐of‐fit tests for Poisson count time series based on the Stein–Chen identity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 35-64, February.
    2. Hassler, Uwe, 2012. "Impulse responses of antipersistent processes," Economics Letters, Elsevier, vol. 116(3), pages 454-456.
    3. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2006. "Estimation of the memory parameter by fitting fractionally differenced autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2101-2130, November.
    4. Farzad Sabzikar & Qiying Wang & Peter C.B. Phillips, 2018. "Asymptotic Theory for Near Integrated Process Driven by Tempered Linear Process," Cowles Foundation Discussion Papers 2131, Cowles Foundation for Research in Economics, Yale University.
    5. Truquet, Lionel, 2023. "Strong mixing properties of discrete-valued time series with exogenous covariates," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 294-317.
    6. Harry Pavlopoulos & George Chronis, 2023. "On highly skewed fractional log‐stable noise sequences and their application," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 337-358, July.
    7. Surgailis, Donatas, 0. "Stable limits of empirical processes of moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 255-274, July.
    8. Datta Gupta, Syamantak & Mazumdar, Ravi R. & Glynn, Peter, 2013. "On the convergence of the spectrum of finite order approximations of stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 1-21.
    9. Peng, Liang & Yao, Qiwei, 2004. "Nonparametric regression under dependent errors with infinite variance," LSE Research Online Documents on Economics 22874, London School of Economics and Political Science, LSE Library.
    10. Bhansali, R. J. & Kokoszka, P. S., 2002. "Computation of the forecast coefficients for multistep prediction of long-range dependent time series," International Journal of Forecasting, Elsevier, vol. 18(2), pages 181-206.
    11. Prasad Bidarkota & J Huston Mcculloch, 2004. "Testing for persistence in stock returns with GARCH-stable shocks," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 256-265.
    12. Guillermo Ferreira & Jorge Mateu & Emilio Porcu, 2018. "Spatio-temporal analysis with short- and long-memory dependence: a state-space approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 221-245, March.
    13. Inoue, Akihiko & Kasahara, Yukio, 2004. "Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 135-147, April.
    14. Aleksandra Grzesiek & Prashant Giri & S. Sundar & Agnieszka WyŁomańska, 2020. "Measures of Cross‐Dependence for Bidimensional Periodic AR(1) Model with α‐Stable Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 785-807, November.
    15. Javier Contreras-Reyes & Wilfredo Palma, 2013. "Statistical analysis of autoregressive fractionally integrated moving average models in R," Computational Statistics, Springer, vol. 28(5), pages 2309-2331, October.
    16. Pilar Grau-Carles, 2005. "Tests of Long Memory: A Bootstrap Approach," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 103-113, February.
    17. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    18. 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).
    19. Arnold, S. & Attinger, S. & Frank, K. & Hildebrandt, A., 2015. "Assessing the structural adequacy of alternative ecohydrological models using a pattern-oriented approach," Ecological Modelling, Elsevier, vol. 316(C), pages 52-61.
    20. Nasari, Masoud M. & Ould-Haye, Mohamedou, 2021. "A consistent estimator for skewness of partial sums of dependent data," Statistics & Probability Letters, Elsevier, vol. 171(C).

    More about this item

    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:bla:jtsera:v:36:y:2015:i:6:p:853-875. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.