order of the nonparametric autoregression (specified by user).
Author
Yulia R. Gel, Vyacheslav Lyubchich, Xingyu Wang
Details
First, autocovariances are estimated
using formula (2.6) by Hall_VanKeilegom_2003;textualfuntimes:
$$\hat{\gamma}(0)=\frac{1}{m_2-m_1+1}\sum_{m=m_1}^{m_2}
\frac{1}{2(n-m)}\sum_{i=m+1}^{n}\{(D_mX)_i\}^2,$$
$$\hat{\gamma}(j)=\hat{\gamma}(0)-\frac{1}{2(n-j)}\sum_{i=j+1}^n\{(D_jX)_i\}^2,$$
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.