# ARest: Estimation of Autoregressive (AR) Parameters In funtimes: Functions for Time Series Analysis

## Description

Estimate parameters φ of autoregressive time series model

X_t = ∑_{i=1}^pφ_iX_{t-i} + e_t,

by default using robust difference-based estimator and Bayesian information criterion (BIC) to select the order p. This function is employed for time series filtering in functions sync_test and wavk_test.

## Usage

 1 ARest(x, ar.order = NULL, ar.method = "HVK", BIC = TRUE) 

## Arguments

 x a vector containing a univariate time series. Missing values are not allowed. ar.order order of autoregressive model when BIC = FALSE, or the maximal order for BIC-based filtering. Default is round(10*log10(length(x))), where x is the time series. ar.method method of estimating autoregression coefficients. Default "HVK" delivers robust difference-based estimates by \insertCiteHall_VanKeilegom_2003;textualfuntimes. Alternatively, options of ar function can be used, such as "burg", "ols", "mle", and "yw". BIC logical value indicates whether the order of autoregressive filter should be selected by Bayesian information criterion (BIC). If TRUE (default), models of orders p= 0,1,...,ar.order or p= 0,1,...,round(10*log10(length(x))) are considered, depending on whether ar.order is defined or not (x is the time series).

## Details

The same formula for BIC is used consistently for all methods:

BIC=n\ln(\hat{σ}^2) + k\ln(n),

where n = length(x), k=p+1.

## Value

A vector of estimated AR coefficients. Returns numeric(0) if the final p=0.

## Author(s)

Vyacheslav Lyubchich

## References

\insertAllCited

ar, HVK, sync_test, wavk_test
  1 2 3 4 5 6 7 8 9 10 11 12 # Fix seed for reproducible simulations: set.seed(1) #Simulate some time series, possibly with trend: n <- 100 Y <- arima.sim(n = n, list(order = c(2, 0, 0), ar = c(-0.7, -0.1))) plot.ts(Y) #Estimate the coefficients: ARest(Y) #HVK by default ARest(Y, ar.method = "yw") #Yule--Walker ARest(Y, ar.method = "burg") #Burg