# Nonlinear forecasting at verying lags using local polynomial regression.

### Description

A wrapper function around `ll.order`

to calculate prediction profiles
(a la Sugihara \& May 1990 and Yao \& Tong 1994). The method uses leave-one-out
cross-validation of the local regression (with CV optimized bandwidth)
against lagged-abundances at various lags.

### Usage

1 2 3 |

### Arguments

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

`step` |
The vector of time steps for predicition. |

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

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

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

### Details

see `ll.order`

for details.

### Value

An object of class "ppll" consisting of a list with the following components:

`step` |
the prediction steps considered. |

`CV` |
the cross-validation error. |

`order` |
the optimal order for each step. |

`bandwidth` |
the otpimal bandwidth for each step. |

`df` |
the degrees of freedom for each step. |

### Author(s)

Ottar N. Bjornstad onb1@psu.edu

### References

Sugihara, G., and May, R.M. (1990) Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734-741

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

Fan, J., Yao, Q., and Tong, H. (1996) Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika, 83, 189-206.

### See Also

`ll.order`

### Examples

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