IDEAS home Printed from https://ideas.repec.org/p/pqs/wpaper/0182005.html
   My bibliography  Save this paper

Hierarchical equilibria of branching populations

Author

Listed:
  • Hao Yu

    (Department of Statistical and Actuarial Sciences, University of Western Ontario)

Abstract

In this paper we study high moment partial sum processes based on residuals of a stationary ARMA model with or without a unknown mean parameter. We show that they can be approximated in probability by the analogous processes which are obtained from the independent and identically distributed (iid) errors of the ARMA model. However, if a unknown mean parameter is used, there will be an additional term that depends on model parameters and a mean estimator. But, when properly normalized, this additional term will be cancelled out. Thus they converge weakly to the same Gaussian processes as if the residuals were iid. Applications to changepoint problems and goodness-of-fit are considered, in particular CUSUM statistics for testing ARMA model structure changes and the Jarque-Bera omnibus statistic for testing normality of the unobservable error distribution of an ARMA model.

Suggested Citation

  • Hao Yu, 2003. "Hierarchical equilibria of branching populations," RePAd Working Paper Series lrsp-TRS391, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0182005
    as

    Download full text from publisher

    File URL: http://www.repad.org/ca/on/lrsp/TRS391.pdf
    File Function: First version, 2003
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    2. J. Kreiss, 1991. "Estimation of the distribution function of noise in stationary processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 285-297, December.
    3. Kulperger, R. J., 1985. "On the residuals of autoregressive processes and polynomial regression," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 107-118, December.
    4. Jushan Bai, 1993. "On The Partial Sums Of Residuals In Autoregressive And Moving Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 247-260, May.
    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. Park, Chul Gyu & Shin, Dong Wan, 1996. "On the asymptotics of residuals in autoregressive moving average processes with one autoregressive unit root," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 341-346, May.
    2. Juncal Cunado & David Gabauer & Rangan Gupta, 2024. "Realized volatility spillovers between energy and metal markets: a time-varying connectedness approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-17, December.
    3. Elie Bouri & Georges Azzi, 2014. "On the Dynamic Transmission of Mean and Volatility across the Arab Stock Markets," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 13(3), pages 279-304, December.
    4. Eric Fur, 2023. "Risk and return of classic car market prices: passion or financial investment?," Journal of Asset Management, Palgrave Macmillan, vol. 24(1), pages 59-68, February.
    5. Georgiev, Iliyan, 2010. "Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables," Journal of Econometrics, Elsevier, vol. 158(1), pages 37-50, September.
    6. Jin, Xiaoye, 2015. "Volatility transmission and volatility impulse response functions among the Greater China stock markets," Journal of Asian Economics, Elsevier, vol. 39(C), pages 43-58.
    7. Lenten, Liam J.A. & Geerling, Wayne & Kónya, László, 2012. "A hedonic model of player wage determination from the Indian Premier League auction: Further evidence," Sport Management Review, Elsevier, vol. 15(1), pages 60-71.
    8. Martha Misas A. & Carlos Esteban Posada P & Diego Mauricio Vásquez E, 2003. "¿Está determinado el nivel de precios por las expectativas de dinero y producto en Colombia?," Revista ESPE - Ensayos Sobre Política Económica, Banco de la República, vol. 21(43), pages 8-31, June.
    9. Bouri, Elie & Gabauer, David & Gupta, Rangan & Tiwari, Aviral Kumar, 2021. "Volatility connectedness of major cryptocurrencies: The role of investor happiness," Journal of Behavioral and Experimental Finance, Elsevier, vol. 30(C).
    10. Evrim Mandacı, Pınar & Cagli, Efe Çaglar & Taşkın, Dilvin, 2020. "Dynamic connectedness and portfolio strategies: Energy and metal markets," Resources Policy, Elsevier, vol. 68(C).
    11. Le, Trung H. & Pham, Linh & Do, Hung X., 2023. "Price risk transmissions in the water-energy-food nexus: Impacts of climate risks and portfolio implications," Energy Economics, Elsevier, vol. 124(C).
    12. Zacharias Psaradakis & Marián Vávra, 2019. "Portmanteau tests for linearity of stationary time series," Econometric Reviews, Taylor & Francis Journals, vol. 38(2), pages 248-262, February.
    13. David Brasington & Don Haurin, 2005. "Capitalization of Parent, School, and Peer Group Components of School Quality into House Price," Departmental Working Papers 2005-04, Department of Economics, Louisiana State University.
    14. Pao, Hsiao-Tien & Fu, Hsin-Chia, 2013. "The causal relationship between energy resources and economic growth in Brazil," Energy Policy, Elsevier, vol. 61(C), pages 793-801.
    15. Ron Bird & Harry Liem & Susan Thorp, 2012. "The Tortoise and the Hare: Risk Premium Versus Alternative Asset Portfolios," Working Paper Series 16, The Paul Woolley Centre for Capital Market Dysfunctionality, University of Technology, Sydney.
    16. Dimitrios Kartsonakis Mademlis & Nikolaos Dritsakis, 2021. "Volatility Forecasting using Hybrid GARCH Neural Network Models: The Case of the Italian Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 11(1), pages 49-60.
    17. Kyritsis, Evangelos & Serletis, Apostolos, 2018. "The zero lower bound and market spillovers: Evidence from the G7 and Norway," Research in International Business and Finance, Elsevier, vol. 44(C), pages 100-123.
    18. Denis Schweizer & Lars Haß & Lutz Johanning & Bernd Rudolph, 2013. "Do Alternative Real Estate Investment Vehicles Add Value to REITs? Evidence from German Open-ended Property Funds," The Journal of Real Estate Finance and Economics, Springer, vol. 47(1), pages 65-82, July.
    19. Kanas, Angelos, 2008. "On real interest rate dynamics and regime switching," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2089-2098, October.
    20. Dungey, Mardi & Milunovich, George & Thorp, Susan & Yang, Minxian, 2015. "Endogenous crisis dating and contagion using smooth transition structural GARCH," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 71-79.

    More about this item

    Keywords

    ARMA; residuals; high moment partial sum process; weak convergence; CUSUM; omnibus; skewness; kurtosis; (sqare root)n consistency.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

    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:pqs:wpaper:0182005. 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: Christian Calmes (email available below). General contact details of provider: https://edirc.repec.org/data/dsuqoca.html .

    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.