HVK: HVK Estimator

In funtimes: Functions for Time Series Analysis

HVK Estimator

Description

Estimate coefficients in nonparametric autoregression using the difference-based approach by \insertCiteHall_VanKeilegom_2003;textualfuntimes.

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 \insertCiteHall_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.

Value

Vector of length ar.order with estimated autoregression coefficients.

Author(s)

Yulia R. Gel, Vyacheslav Lyubchich, Xingyu Wang

References

\insertAllCited

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)

funtimes documentation built on March 31, 2023, 7:35 p.m.