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ARest: 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 functions sync_test and wavk_test.

Usage

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

Value

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

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 Hall_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).

Author

Vyacheslav Lyubchich

Details

The same formula for BIC is used consistently for all methods: $$BIC=n\ln(\hat{\sigma}^2) + k\ln(n),$$ where \(n\) = length(x), \(k=p+1\).

References

See Also

ar, HVK, 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