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Lack-of-fit of a parametric measurement error AR(1) model

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  • Balakrishna, N.
  • Kim, Jiwoong
  • Koul, Hira L.

Abstract

This paper proposes an asymptotically distribution free test for fitting a parametric model to the autoregressive function in the AR(1) model in the presence of measurement error. The test is based on a martingale transform of a certain marked residual empirical process. A simulation study assessing the finite sample level and power performance of the proposed test is also included.

Suggested Citation

  • Balakrishna, N. & Kim, Jiwoong & Koul, Hira L., 2020. "Lack-of-fit of a parametric measurement error AR(1) model," Statistics & Probability Letters, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:stapro:v:166:y:2020:i:c:s0167715220301759
    DOI: 10.1016/j.spl.2020.108872
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    References listed on IDEAS

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    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    2. Staudenmayer, John & Buonaccorsi, John P., 2005. "Measurement Error in Linear Autoregressive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 841-852, September.
    3. Tanaka, Katsuto, 2002. "A Unified Approach To The Measurement Error Problem In Time Series Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 278-296, April.
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    5. Pfeffermann, Danny & Feder, Moshe & Signorelli, David, 1998. "Estimation of Autocorrelations of Survey Errors with Application to Trend Estimation in Small Areas," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 339-348, July.
    6. N. Balakrishna & H. L. Koul & M. Ossiander & L. Sakhanenko, 2019. "Fitting a pth Order Parametric Generalized Linear Autoregressive Multiplicative Error Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 103-122, September.
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