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

 ARest R Documentation

## Estimation of Autoregressive (AR) Parameters

### Description

Estimate parameters \phi of autoregressive time series model

X_t = \sum_{i=1}^p\phi_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 the functions notrend_test, sync_test, and wavk_test.

### Usage

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 \insertCiteHall_VanKeilegom_2003;textualfuntimes. 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.

### Details

The formula for information criteria used consistently for all methods:

IC=n\ln(\hat{\sigma}^2) + (p + 1)k,

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).

### Value

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

### Author(s)

Vyacheslav Lyubchich

### References

\insertAllCited

ar, HVK, notrend_test, sync_test, wavk_test

### 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



funtimes documentation built on March 31, 2023, 7:35 p.m.