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

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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

`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).

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.

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

Vyacheslav Lyubchich

\insertAllCited

ar, HVK, sync_test, wavk_test

# 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