HVK {funtimes}

HVK Estimator

Description

Estimate coefficients in nonparametric 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 nonparametric autoregression (specified by user).

Details

First, autocovariances are estimated using 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.

Value

Vector of length ar.order with estimated autoregression coefficients.

Author(s)

Yulia R. Gel, Vyacheslav Lyubchich, Xingyu Wang

References

Hall P, 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(2), 443–456. doi:10.1111/1467-9868.00395.

See Also

ar, ARest

Examples

X <- arima.sim(n = 300, list(order = c(1, 0, 0), ar = c(0.6)))
HVK(as.vector(X), ar.order = 1)