IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1916.html
   My bibliography  Save this paper

Norming Rates and Limit Theory for Some Time-Varying Coefficient Autoregressions

Author

Abstract

A time-varying autoregression is considered with a similarity-based coefficient and possible drift. It is shown that the random walk model has a natural interpretation as the leading term in a small-sigma expansion of a similarity model with an exponential similarity function as its autoregressive coefficient. Consistency of the quasi-maximum likelihood estimator of the parameters in this model is established, the behaviors of the score and Hessian functions are analyzed and test statistics are suggested. A complete list is provided of the normalization rates required for the consistency proof and for the score and Hessian functions standardization. A large family of unit root models with stationary and explosive alternatives are characterized within the similarity class through the asymptotic negligibility of a certain quadratic form that appears in the score function. A variant of the stochastic unit root model within the class is studied and a large sample limit theory provided which leads to a new nonlinear diffusion process limit showing the form of the drift and conditional volatility induced by this model. Some simulations and a brief empirical application to data on an Australian Exchange Traded Fund are included.

Suggested Citation

  • Offer Lieberman & Peter C.B. Phillips, 2013. "Norming Rates and Limit Theory for Some Time-Varying Coefficient Autoregressions," Cowles Foundation Discussion Papers 1916, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1916
    as

    Download full text from publisher

    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d19/d1916.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    2. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    3. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    4. Lundbergh, Stefan & Terasvirta, Timo & van Dijk, Dick, 2003. "Time-Varying Smooth Transition Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 104-121, January.
    5. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," Review of Economic Studies, Oxford University Press, vol. 37(4), pages 537-542.
    6. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(04), pages 888-947, August.
    7. Levy, Ariel & Lieberman, Offer, 2013. "Overreaction of country ETFs to US market returns: Intraday vs. daily horizons and the role of synchronized trading," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1412-1421.
    8. R. Dahlhaus & M. Neumann & R. von Sachs, 1997. "Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes," SFB 373 Discussion Papers 1997,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. S. Y. Hwang & I. V. Basawa, 2005. "Explosive Random-Coefficient AR(1) Processes and Related Asymptotics for Least-Squares Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 807-824, November.
    10. Offer Lieberman, 2012. "A similarity‐based approach to time‐varying coefficient non‐stationary autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 484-502, May.
    11. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-737, September.
    12. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-1269, September.
    13. Lieberman, Offer, 2010. "Asymptotic Theory For Empirical Similarity Models," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1032-1059, August.
    14. Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
    15. Leybourne, S J & McCabe, B P M & Tremayne, A R, 1996. "Can Economic Time Series Be Differenced to Stationarity?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 435-446, October.
    16. Nicholls, D. F. & Quinn, B. G., 1981. "The estimation of multivariate random coefficient autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 544-555, December.
    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. Lieberman, Offer & Phillips, Peter C.B., 2017. "A multivariate stochastic unit root model with an application to derivative pricing," Journal of Econometrics, Elsevier, vol. 196(1), pages 99-110.
    2. Kinjo Keita & Sugawara Shinya, 2016. "Predicting Empirical Patterns in Viewing Japanese TV Dramas Using Case-Based Decision Theory," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(2), pages 679-709, June.
    3. Yubo Tao & Peter C.B. Phillips & Jun Yu, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Cowles Foundation Discussion Papers 2114, Cowles Foundation for Research in Economics, Yale University.
    4. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Economics and Statistics Working Papers 18-2017, Singapore Management University, School of Economics.
    5. Offer Lieberman & Peter C.B. Phillips, 2016. "IV and GMM Estimation and Testing of Multivariate Stochastic Unit Root Models," Cowles Foundation Discussion Papers 2061, Cowles Foundation for Research in Economics, Yale University.
    6. repec:gam:jecnmx:v:6:y:2018:i:3:p:39-:d:165046 is not listed on IDEAS

    More about this item

    Keywords

    Autoregression; Consistency; Nonlinear diffusion; Nonstationarity; Similarity; Small sigma approximation; Stochastic unit root; Time-varying coefficients;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:cwl:cwldpp:1916. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Regan). General contact details of provider: http://edirc.repec.org/data/cowleus.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.