Description Usage Arguments Details Value References Examples

A function to estimate the order of a time series using the nonparametric order selection method of Cheng and Tong (1992, 1994) as modified by Yao & Tong (1994; see also Fan, Yao & Tong 1996). The method uses leave-one-out cross-validation of the locally linear regression against lagged-abundances.

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`x` |
A time series without missing values. |

`order` |
The candidate orders. The default is 1:5. |

`step` |
The time step for prediction. |

`deg` |
The degree of the local polynomial. |

`bandwidth` |
The candidate bandwidths to be considered. |

`cv` |
if TRUE leave-one-out cross-validation will be performed. |

`echo` |
if TRUE a counter shows the progress |

The time series is normalized prior to cross-validation.

A Gaussian kernel is used for the locally linear regression.

The bandwidth is optimized using cross-validation. If a single bandwidth is provided, no cross validation of bandwidth will be carried out. Highly nonlinear data will require more narrow bandwidths. If NA is returned it may be because the min bandwidth considered is too small relative to the density of data.

Missing values are NOT permitted.

If `deg`

is set to 0, the order is estimated on the basis of the
Nadaraya-Watson (locally constant) estimator of the conditional expectation
against lagged-abundances (Cheng and Tong 1992, 1994).

An object of class "ll.order" is returned consisting of the following components:

`grid` |
the grid of orders, bandwidths, and CV's. |

`grid$order` |
the orders. |

`grid$CV` |
the cross-validation score
across the grid of orders and bandwidths. (If |

`grid$GCV` |
the generalized cross-validation score. |

`grid$bandwidth` |
the bandwidths. |

`grid$df` |
the degrees of freedom of the fitted model. |

`order` |
the vector of orders considered. |

`deg` |
The degree of the local polynomial. |

Cheng, B. & Tong, H. (1992) On consistent nonparametric order determination and chaos. Journal of Royal Statistical Society B, 54, 427-449.

Cheng, B. & Tong, H. (1994) Orthogonal projection, embedding dimension and sample size in chaotic time series from a statistical perspective. Philosophical Transactions of the Royal Society London, A. , 348, 325-341. https://doi.org/10.1098/rsta.1994.0094

Fan, J., Yao, Q., & Tong, H. (1996) Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika, 83, 189-206. ttps://doi.org/10.1093/biomet/83.1.189

Yao, Q. & Tong, H. (1994) Quantifying the influence of initial values on non-linear prediction. Journal of Royal Statistical Society B, 56, 701-725.

Bjornstad, O.N., Sait, S.M., Stenseth, N.C., Thompson, D.J., & Begon, M. (2001) Coupling and the impact of specialised enemies on the dimensionality of prey dynamics. Nature, 409, 1001-1006. https://doi.org/10.1038/35059003

Loader, C. (1999) Local Regression and Likelihood. Springer, New York. https://doi.org/10.1007/b98858

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