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**Least-squares parameter estimation algorithm for a class of input nonlinear systems.**
*(English)*
Zbl 1251.62036

Summary: We study least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

### MSC:

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62F12 | Asymptotic properties of parametric estimators |

65C60 | Computational problems in statistics (MSC2010) |

### Keywords:

input nonlinear controlled autoregressive model; input nonlinear controlled autoregressive autoregressive moving average model
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\textit{W. Xiong} et al., J. Appl. Math. 2012, Article ID 684074, 14 p. (2012; Zbl 1251.62036)

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### References:

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