IDEAS home Printed from https://ideas.repec.org/a/spt/stecon/v6y2017i1f6_1_4.html
   My bibliography  Save this article

Asymptotic relationship between sample mean and sample variance for autoregressive processes of order 1

Author

Listed:
  • Athanase Polymenis

Abstract

Autoregressive processes of order 1 (or AR(1) processes) have been extensively used in econometrics and time series literature. Noting that an early important result concerning the sample mean 𝑈 and variance 𝑆 of independent normally distributed random variables 𝑈 with equal means and variances is that 𝑈 and 𝑆 are independent, the present article investigates whether this result can be extended to AR(1) non-stationary processes as the sample size becomes very large. To this end, a property called “asymptotic stationarity†is used for algebraic calculations. A result for asymptotic independence concerning the sample mean and variance is then adequately derived for these types of processes.Mathematics Subject Classification: 62E20; 62M10Keywords: Autoregressive process; Asymptotic stationarity; Asymptotic independence

Suggested Citation

  • Athanase Polymenis, 2017. "Asymptotic relationship between sample mean and sample variance for autoregressive processes of order 1," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-4.
  • Handle: RePEc:spt:stecon:v:6:y:2017:i:1:f:6_1_4
    as

    Download full text from publisher

    File URL: http://www.scienpress.com/Upload/JSEM%2fVol%206_1_4.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Spanos,Aris, 1986. "Statistical Foundations of Econometric Modelling," Cambridge Books, Cambridge University Press, number 9780521269124, October.
    2. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    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. Glaser, Markus, 2003. "Online Broker Investors: Demographic Information, Investment Strategy, Portfolio Positions, and Trading Activity," Sonderforschungsbereich 504 Publications 03-18, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    2. Psaradakis, Zacharias & Sola, Martin, 1996. "On the power of tests for superexogeneity and structural invariance," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 151-175.
    3. McGuirk, Anya M. & Spanos, Aris, 2004. "Revisiting Error Autocorrelation Correction: Common Factor Restrictions And Granger Causality," 2004 Annual meeting, August 1-4, Denver, CO 20176, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    5. Glaser, Markus & Weber, Martin, 2007. "Why inexperienced investors do not learn: They do not know their past portfolio performance," Finance Research Letters, Elsevier, vol. 4(4), pages 203-216, December.
    6. Markus Glaser & Martin Weber, 2007. "Overconfidence and trading volume," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 32(1), pages 1-36, June.
    7. Glaser, Markus & Weber, Martin, 2009. "Which past returns affect trading volume?," Journal of Financial Markets, Elsevier, vol. 12(1), pages 1-31, February.
    8. Markus Glaser & Martin Weber, 2005. "September 11 and Stock Return Expectations of Individual Investors," Review of Finance, Springer, vol. 9(2), pages 243-279, June.
    9. Kapteyn, Arie & Kalwij, Adriaan & Zaidi, Asghar, 2004. "The myth of worksharing," Labour Economics, Elsevier, vol. 11(3), pages 293-313, June.
    10. Glaser, Markus, 2003. "Online broker investors : demographic information, investment strategy, portfolio positions, and trading activity," Papers 03-18, Sonderforschungsbreich 504.
    11. McGuirk, Anya M. & Spanos, Aris, 2002. "The Linear Regression Model With Autocorrelated Errors: Just Say No To Error Autocorrelation," 2002 Annual meeting, July 28-31, Long Beach, CA 19905, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    12. Charles G. Renfro, 2009. "The Practice of Econometric Theory," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75571-5, July-Dece.
    13. Jeffrey Edwards, 2006. "Politics, Inflation, and the Mundell-Tobin Effect," Journal of Economic Insight, Missouri Valley Economic Association, vol. 32(2), pages 9-30.
    14. Idris Djouahra, 2022. "Conceptual understanding of linear regression among economics students at the university center of Tipaza, Algeria," Croatian Review of Economic, Business and Social Statistics, Sciendo, vol. 8(2), pages 66-83, December.
    15. Fernando A. López & Román Mínguez & Jesús Mur, 2020. "ML versus IV estimates of spatial SUR models: evidence from the case of Airbnb in Madrid urban area," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(2), pages 313-347, April.
    16. Mizon, Grayham E., 1995. "A simple message for autocorrelation correctors: Don't," Journal of Econometrics, Elsevier, vol. 69(1), pages 267-288, September.
    17. Anya McGuirk & Aris Spanos, 2009. "Revisiting Error‐Autocorrelation Correction: Common Factor Restrictions and Granger Non‐Causality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(2), pages 273-294, April.
    18. Hillebrand, Eric & Schnabl, Gunther & Ulu, Yasemin, 2009. "Japanese foreign exchange intervention and the yen-to-dollar exchange rate: A simultaneous equations approach using realized volatility," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(3), pages 490-505, July.
    19. Anikó Bíró, 2013. "Subjective mortality hazard shocks and the adjustment of consumption expenditures," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1379-1408, October.
    20. Zanini, Fabio C. & Irwin, Scott H. & Schnitkey, Gary D. & Sherrick, Bruce J., 2000. "Estimating Farm-Level Yield Distributions For Corn And Soybeans In Illinois," 2000 Annual meeting, July 30-August 2, Tampa, FL 21720, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    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:spt:stecon:v:6:y:2017:i:1:f:6_1_4. 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: Eleftherios Spyromitros-Xioufis (email available below). General contact details of provider: http://www.scienpress.com/ .

    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.