IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/948.html
   My bibliography  Save this paper

Operational Algebra and Regression t-Tests

Author

Abstract

Data reduction involves a physical transition from sample data to econometric estimator and test statistic. This transition induces a mapping on the probability law of the sample, whose image is the distribution of the statistic of interest. At a general level, the mapping can often be captured by means of an operational algebra. Some methods than employ nonlinear functions of differential operators are suggested which can perform this task. The methods are related to pseudodifferential operator techniques that are used in abstract mathematics to solve systems of partial differential equations. They also generalize the fractional calculus methods developed by the author in earlier work (1984, 1985). Two examples are studied in detail. One of these deals with the feasible generalized least squares estimator and its regression t-statistic in the linear model with a non scalar error covariance matrix whose elements are functions of a finite dimensional vector of nuisance parameters. This includes a wide class of models such as general SUR systems and models with serially dependent or heterogeneous errors.

Suggested Citation

  • Peter C.B. Phillips, 1990. "Operational Algebra and Regression t-Tests," Cowles Foundation Discussion Papers 948, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:948
    Note: CFP 830.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d09/d0948.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Phillips, P.C.B., 1984. "The exact distribution of the Stein-rule estimator," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 123-131.
    2. Zinde-Walsh, Victoria, 1988. "Some Exact Formulae for Autoregressive Moving Average Processes," Econometric Theory, Cambridge University Press, vol. 4(3), pages 384-402, December.
    3. Rothenberg, Thomas J, 1984. "Approximate Normality of Generalized Least Squares Estimates," Econometrica, Econometric Society, vol. 52(4), pages 811-825, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2005. "Improved HAR Inference," Cowles Foundation Discussion Papers 1513, Cowles Foundation for Research in Economics, Yale University.

    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. Phillips, P C B, 1986. "The Exact Distribution of the Wald Statistic," Econometrica, Econometric Society, vol. 54(4), pages 881-895, July.
    2. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    3. Richard C.K. Burdekin, 1992. "Assessing the Impact of US Macroeconomic Policies and Inflation Rates on the Australian Economy," The Economic Record, The Economic Society of Australia, vol. 68(1), pages 16-30, March.
    4. David F. Findley & Demetra P. Lytras & Agustin Maravall, 2016. "Illuminating ARIMA model-based seasonal adjustment with three fundamental seasonal models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 11-52, March.
    5. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June.
    6. Koenker, Roger & Machado, Jose A. F., 1998. "The Falstaff estimator," Economics Letters, Elsevier, vol. 61(1), pages 23-28, October.
    7. Wan, Alan T. K. & Chaturvedi, Anoop, 2001. "Double k-Class Estimators in Regression Models with Non-spherical Disturbances," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 226-250, November.
    8. Nelson C. Mark & Donggyu Sul, 2004. "The Use of Predictive Regressions at Alternative Horizons in Finance and Economics," Finance 0409032, University Library of Munich, Germany.
    9. Rayner, Robert K., 1991. "Resampling methods for tests in regression models with autocorrelated errors," Economics Letters, Elsevier, vol. 36(3), pages 281-284, July.
    10. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    11. Hausman, Jerry & Kuersteiner, Guido, 2008. "Difference in difference meets generalized least squares: Higher order properties of hypotheses tests," Journal of Econometrics, Elsevier, vol. 144(2), pages 371-391, June.
    12. Banerjee, Anurag N. & Magnus, Jan R., 2000. "On the sensitivity of the usual t- and F-tests to covariance misspecification," Journal of Econometrics, Elsevier, vol. 95(1), pages 157-176, March.
    13. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    14. Linton, Oliver, 1997. "An Asymptotic Expansion in the GARCH(l, 1) Model," Econometric Theory, Cambridge University Press, vol. 13(4), pages 558-581, February.
    15. Kezdi, Gabor & Hahn, Jinyong & Solon, Gary, 2002. "Jackknife minimum distance estimation," Economics Letters, Elsevier, vol. 76(1), pages 35-45, June.
    16. Wilfredo Palma & Mauricio Zevallos, 2004. "Analysis of the correlation structure of square time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 529-550, July.
    17. Paulina Granados Z., 2004. "Chilean Household Income Function: Life Cycle and Persistence of Shocks," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 7(1), pages 51-89, April.
    18. repec:bla:ecorec:v:64:y:1988:i:185:p:81-101 is not listed on IDEAS
    19. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.
    20. Choudhury, Askar H. & Power, Simon, 1995. "A new approximate GLS estimator for the linear regression model with ARMA(p, q) disturbances," Economics Letters, Elsevier, vol. 48(2), pages 119-127, May.
    21. Galbraith, JohnW. & Zinde-Walsh, Victoria, 1999. "On the distributions of Augmented Dickey-Fuller statistics in processes with moving average components," Journal of Econometrics, Elsevier, vol. 93(1), pages 25-47, November.

    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:cwl:cwldpp:948. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.