# Estimation of AR Models by Robust Filtering

### Description

Robustly estimates AR models using a robust filter algorithm. See Dürre et al. (2014) for details.

### Usage

1 |

### Arguments

`timeseries` |
univariate numeric vector or time series object. |

`p` |
numeric determining the order of the AR fit. |

`psi.l` |
numeric determining the used psi function, see details. |

`psi.0` |
numeric determining the used psi function, see details. |

`aicpenalty` |
function of p, indicating the penalty for a larger model, see details. |

### Details

The function fits AR models of increasing order by a robust version of the Durbin Levinson algorithm as described in chapter 8 of Maronna et al. (2006). The AR coefficients are estimated by minimizing a robust scale (`scaleTau2`

) of one step ahead residuals of robustly filtered predictors. The filter process basically compares the predicted value under the estimated model with the observed one and transformes the corresponding residual with the psi function. The transformed value is then set to the sum of the predicted value and the transformed residual. For more details see Maronna et al. (2006) and Dürre et al. (2014).

Following Maronna et al. (2006), the psi function should fulfill two properties. It should be the identity for small absolute values and 0 for large absolute values. Both thresholds can be determined by `psi.l`

and `psi.0`

. Here the psi function is choosen to be two times continuous differentiable, see Dürre et al. (2014) for a formal definition.

### Value

List containing the following values

`partial autocorrelations` |
matrix representing the successive estimated partial correlations of the model. In the first column are the partial correlations of the AR model of order 1 and so on. |

`variance of innovations` |
numeric containing the successive scale estimation of the residuals of the successive AR models. The first entry is for the AR(1) model and so on. |

`autocorrelation` |
numeric of estimated acf up until lag p. |

`aic` |
numeric of aic values of successive AR models. |

`robustly filtered timeseries` |
matrix containing the robustly filtered time series of successive AR models. The first column corresponds to the AR(1) model and so on. |

`AR-coefficients` |
matrix containing the estimated AR coefficients of successive AR models. The first column corresponds to the AR(1) model and the first row to the first AR coefficient and so on. |

### Author(s)

Alexander Dürre, Tobias Liboschik and Jonathan Rathjens

### References

Dürre, A., Fried, R. and Liboschik, T. (2015): Robust estimation of (partial) autocorrelation, *Wiley Interdisciplinary Reviews: Computational Statistics*, vol. 7, 205–222.

Maronna, R., Martin, D. and Yohai, V. (2006): *Robust statistics*, Wiley, Chichester.

### See Also

The wrapper function `arrob`

.

### Examples

1 2 3 |

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