# HVK: HVK Estimator In funtimes: Functions for Time Series Analysis

 HVK R Documentation

## 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, Yuleâ€“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

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