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Additive models with autoregressive symmetric errors based on penalized regression splines

Author

Listed:
  • Rodrigo A. Oliveira

    (Universidade Federal de Goiás)

  • Gilberto A. Paula

    (Universidade de São Paulo)

Abstract

In this paper additive models with p-order autoregressive conditional symmetric errors based on penalized regression splines are proposed for modeling trend and seasonality in time series. The aim with this kind of approach is try to model the autocorrelation and seasonality properly to assess the existence of a significant trend. A backfitting iterative process jointly with a quasi-Newton algorithm are developed for estimating the additive components, the dispersion parameter and the autocorrelation coefficients. The effective degrees of freedom concerning the fitting are derived from an appropriate smoother. Inferential results and selection model procedures are proposed as well as some diagnostic methods, such as residual analysis based on the conditional quantile residual and sensitivity studies based on the local influence approach. Simulations studies are performed to assess the large sample behavior of the maximum penalized likelihood estimators. Finally, the methodology is applied for modeling the daily average temperature of San Francisco city from January 1995 to April 2020.

Suggested Citation

  • Rodrigo A. Oliveira & Gilberto A. Paula, 2021. "Additive models with autoregressive symmetric errors based on penalized regression splines," Computational Statistics, Springer, vol. 36(4), pages 2435-2466, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01106-2
    DOI: 10.1007/s00180-021-01106-2
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    References listed on IDEAS

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    1. Huang, Lei & Jiang, Hui & Wang, Huixia, 2019. "A novel partial-linear single-index model for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 110-122.
    2. Chun-Zheng Cao & Jin-Guan Lin & Li-Xing Zhu, 2010. "Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors," Statistical Papers, Springer, vol. 51(4), pages 813-836, December.
    3. Germán Ibacache-Pulgar & Gilberto Paula & Francisco Cysneiros, 2013. "Semiparametric additive models under symmetric distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 103-121, March.
    4. Paula, Gilberto A. & Medeiros, Marcio & Vilca-Labra, Filidor E., 2009. "Influence diagnostics for linear models with first-order autoregressive elliptical errors," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 339-346, February.
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    8. Cysneiros, Francisco Jose A. & Paula, Gilberto A., 2005. "Restricted methods in symmetrical linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 689-708, June.
    9. Lee, Sik-Yum & Xu, Liang, 2004. "Influence analyses of nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 321-341, March.
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    Cited by:

    1. Yonghui Liu & Jiawei Lu & Gilberto A. Paula & Shuangzhe Liu, 2025. "Bayesian diagnostics in a partially linear model with first-order autoregressive skew-normal errors," Computational Statistics, Springer, vol. 40(2), pages 1021-1051, February.
    2. Shu Wei Chou-Chen & Rodrigo A. Oliveira & Irina Raicher & Gilberto A. Paula, 2024. "Additive partial linear models with autoregressive symmetric errors and its application to the hospitalizations for respiratory diseases," Statistical Papers, Springer, vol. 65(8), pages 5145-5166, October.

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