ARest function

Estimation of Autoregressive (AR) Parameters

Estimate parameters $\phi$ of autoregressive time series model [REMOVE_ME]$X_t = \sum_{i=1}^p\phi_iX_{t-i} + e_t, [REMOVE_ME_2]$

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 the functions notrend_test, sync_test, and wavk_test.

ARest(x, ar.order = NULL, ar.method = "HVK", ic = c("BIC", "AIC", "none"))

Arguments

• x: a vector containing a univariate time series. Missing values are not allowed.
• ar.order: order of the autoregressive model when ic = "none", or the maximal order for IC-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 if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="Hall_VanKeilegom_2003;textual",package="funtimes",cached_env=.Rdpack.currefs) . Alternatively, options of ar function can be used, such as "burg", "ols", "mle", and "yw".
• ic: information criterion used to select the order of autoregressive filter (AIC of BIC), considering models of orders $p=$ 0,1,...,ar.order. If ic = "none", the AR($p$) model with $p=$ ar.order is used, without order selection.

Returns

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

Description

Estimate parameters $\phi$ of autoregressive time series model

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 the functions notrend_test, sync_test, and wavk_test.

Details

The formula for information criteria used consistently for all methods:

where $n$ = length(x), $p$ is the autoregressive order ($p + 1$ is the number of model parameters), and $k$ is the penalty ($k = \ln(n)$ in BIC, and $k = 2$ in AIC).

Examples

# Simulate a time series Y:
Y <- arima.sim(n = 200, 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

References

if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_all_ref(.Rdpack.currefs)

See Also

ar, HVK, notrend_test, sync_test, wavk_test

Author(s)

Vyacheslav Lyubchich