order of the non-parametric autoregression (specified by user).
Value
Vector of length ar.order with estimated autoregression coefficients.
Details
First, autocovariances are estimated (formula (2.6) by Hall and Van Keilegom, 2003):
$$\hat{\gamma}(0)=\frac{1}{m_2-m_1+1}\sum_{m=m_1}^{m_2}\frac{1}{2(n-m)}\sum_{i=m+1}^{n}{(D_mX)_i}^2,$$
$$\hat{\gamma}(j)=\hat{\gamma}(0)-\frac{1}{2(n-j)}\sum_{i=j+1}^n{(D_jX)_i}^2,$$
where $n$=length(X) is sample size, $D_j$ is a difference operator such that $(D_jX)_i=X_i-X_{i-j}$.
Then, Yule-Walker method is used to derive autoregression coefficients.
References
Hall, P. and Van Keilegom, I. (2003) Using difference-based methods for inference in nonparametric regression with time series errors. J. R. Statist. Soc. B 65, Part 2, 443--456.