funtimes (version 5.0)

HVK: HVK Estimator

Description

Estimates coefficients in non-parametric autoregression using the difference-based approach by Hall and Van Keilegom (2003).

Usage

HVK(X, m1 = NULL, m2 = NULL, ar.order = 1)

Arguments

X

univariate time series. Missing values are not allowed.

m1, m2

subsidiary smoothing parameters. Default m1 = round(length(X)^(0.1)), m2 = round(length(X)^(0.5)).

ar.order

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. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65: 443--456. DOI: 10.1111/1467-9868.00395

Examples

# NOT RUN {
X <- arima.sim(n = 300, list(order = c(1, 0, 0), ar = c(0.6)))
HVK(as.vector(X), ar.order = 1)
# }