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Iterated Partial Sum Sequences of Regression Residuals and Tests for Changepoints with Continuity Constraints

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  • V. K. Jandhyala
  • I. B. MacNeill

Abstract

Iterated partial sum sequences of regression least squares residuals are defined and large sample properties of sequences of stochastic processes defined by these iterated partial sums are discussed. Also, finite sample properties of the iterated partial sum sequences are obtained. These include a property of least squares residuals of polynomial fits to equispaced data, namely the iterated partial sums sum to 0 provided that the order of iteration is not greater than the order of the polynomial, thus extending the well‐known result that residuals sum to 0. Iterated partial sums are shown to play an important role in testing regression parameters for changes at unknown times under the constraint of continuity.

Suggested Citation

  • V. K. Jandhyala & I. B. MacNeill, 1997. "Iterated Partial Sum Sequences of Regression Residuals and Tests for Changepoints with Continuity Constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 147-156.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:1:p:147-156
    DOI: 10.1111/1467-9868.00060
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    Cited by:

    1. Anestis Antoniadis & Irène Gijbels & Mila Nikolova, 2011. "Penalized likelihood regression for generalized linear models with non-quadratic penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 585-615, June.
    2. Aue, Alexander & Horváth, Lajos & Hušková, Marie, 2012. "Segmenting mean-nonstationary time series via trending regressions," Journal of Econometrics, Elsevier, vol. 168(2), pages 367-381.
    3. Aue, Alexander & Horvth, Lajos & Huskov, Marie, 2009. "Extreme value theory for stochastic integrals of Legendre polynomials," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1029-1043, May.
    4. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.

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