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

## Description

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

## Usage

 1 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).

## Details

First, autocovariances are estimated using formula (2.6) by \insertCiteHall_VanKeilegom_2003;textualfuntimes:

\hat{γ}(0)=\frac{1}{m_2-m_1+1}∑_{m=m_1}^{m_2} \frac{1}{2(n-m)}∑_{i=m+1}^{n}\{(D_mX)_i\}^2,

\hat{γ}(j)=\hat{γ}(0)-\frac{1}{2(n-j)}∑_{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

ar, ARest
 1 2 X <- arima.sim(n = 300, list(order = c(1, 0, 0), ar = c(0.6))) HVK(as.vector(X), ar.order = 1)