R: Consistent nonlinear estimate of the order using local...
ll.order
R Documentation
Consistent nonlinear estimate of the order
using local polynomial regression.
Description
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.
if TRUE leave-one-out crossvalidation will be performed.
echo
if TRUE a counter shows the progress
Details
The time series is normalized prior to cross-validation.
A Gaussian kernel is used for the locally linear regression.
The bandwidth is optimized using crossvalidation. 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 expecation against lagged-abundances
(Cheng and Tong 1992, 1994). The function subsumes
the nw.order of the previous S-plus nlt-library.
The function requires Loader's locfit-library.
Value
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 cv = TRUE).
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.
Fan, J., Yao, Q., & Tong, H. (1996) Estimation of
conditional densities and sensitivity measures
in nonlinear dynamical systems. Biometrika, 83, 189-206.
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.
Loader, C. (1999) Local Regression and Likelihood.
Springer, New York.
See Also
summary.ll.orderplot.ll.order
Examples
data(plodia)
fit1 <- ll.order(sqrt(plodia), order=1:3, bandwidth
= seq(0.5, 1.5, by = 0.5))
## Not run: plot.ll.order(fit1)
summary.ll.order(fit1)