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On the residuals of autoregressive processes and polynomial regression

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  • Kulperger, R. J.

Abstract

The residual processes of a stationary AR(p) process and of polynomial regression are considered. The residuals are obtained from ordinary least squares fitting. In the AR case, the partial sums converge to Brownian motion. In the polynomial case, they converge to generalized Brownian bridges. Other uses of the residuals are considered. Parameter estimation based on approximate log likelihood function of the residuals is considered.

Suggested Citation

  • Kulperger, R. J., 1985. "On the residuals of autoregressive processes and polynomial regression," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 107-118, December.
    • Handle: RePEc:eee:spapps:v:21:y:1985:i:1:p:107-118
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    Cited by:

    1. Muriel, Nelson & González-Farías, Graciela, 2018. "Testing the null of difference stationarity against the alternative of a stochastic unit root: A new test based on multivariate STUR," Econometrics and Statistics, Elsevier, vol. 7(C), pages 46-62.
    2. Claudia Kirch & Birte Muhsal & Hernando Ombao, 2015. "Detection of Changes in Multivariate Time Series With Application to EEG Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1197-1216, September.
    3. Hao Yu, 2003. "Hierarchical equilibria of branching populations," RePAd Working Paper Series lrsp-TRS391, Département des sciences administratives, UQO.
    4. Park, Chul Gyu & Shin, Dong Wan, 1996. "On the asymptotics of residuals in autoregressive moving average processes with one autoregressive unit root," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 341-346, May.
    5. Alejandra Cabaña & Enrique M. Cabaña & Marco Scavino, 2012. "Weak Convergence of Marked Empirical Processes for Focused Inference on AR(p) vs AR(p + 1) Stationary Time Series," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 793-810, September.

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