# prediction.profile.ll: Nonlinear forecasting at verying lags using local polynomial... In nlts: (Non)Linear Time Series Analysis

## 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``` ``` prediction.profile.ll(x, step = 1:10, order = 1:5, deg = 2, bandwidth = c(seq(0.3, 1.5, by = 0.1), 2:10)) ```

## 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.

## 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.

`ll.order`
 ```1 2 3 4 5 6``` ``` data(plodia) fit1 <- prediction.profile.ll(sqrt(plodia), step=1:3, order=1:3, bandwidth = seq(0.5, 1.5, by = 0.5)) ## Not run: plot.ppll(fit1) ```