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Lag selection in stochastic additive models

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  • Shuping Jiang
  • Lan Xue

Abstract

We studied stochastic additive models (SAM) for nonlinear time series data. We proposed a penalised polynomial spline (PPS) method for estimation and lag selection in SAM. This method approximated the nonparametric functions by polynomial splines and performed variable/lag selection by imposing a penalty on the empirical L 2 norm of the spline functions. Under geometrically α-mixing condition, we established that the resulting estimator converges at the same rate as in univariate smoothing. Our method also selected the correct model with probability approaching to one as the sample size increased. A coordinate-wise algorithm was developed for finding the solution of the PPS problem. Extensive Monte Carlo studies had been conducted and showed that the proposed procedure worked effectively even with moderate sample size. We also illustrated the proposed method by analysing the US employment time series.

Suggested Citation

  • Shuping Jiang & Lan Xue, 2013. "Lag selection in stochastic additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 129-146, March.
  • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:129-146
    DOI: 10.1080/10485252.2012.754440
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    Cited by:

    1. Shuping Jiang & Lan Xue, 2015. "Globally consistent model selection in semi-parametric additive coefficient models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 532-551, December.
    2. Miao Yang & Lan Xue & Lijian Yang, 2016. "Variable selection for additive model via cumulative ratios of empirical strengths total," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 595-616, September.

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