This function builds three varieties of the mean-value chronology, including
the ARSTAN chronology, typically from a
data.frame of detrended ring widths as produced by
detrend.
chron.ars(rwi, biweight=TRUE, maxLag=10, firstAICmin=TRUE,
verbose=TRUE, prewhitenMethod=c("ar.yw","arima.CSS-ML"))A data.frame of class "crn" with the following columns:
the standard chronology: the (biweight) mean ring-width index across all series for each year.
the residual chronology: the standard chronology after multivariate autoregressive prewhitening to remove common persistence.
the ARSTAN chronology: the residual chronology with the
pooled autoregression reintroduced. When the selected AR order is
zero, std, res, and ars are identical.
the number of series with non-missing values in each year.
Row names are the years taken from rownames(rwi).
a data.frame of (usually detrended) ring widths with
rownames(rwi) containing years and colnames(rwi)
containing each series ID such as produced by
detrend
logical flag. If TRUE then a robust
mean is calculated using tbrm.
an integer giving the maximum lag to consider in
the pooled AR modeling. If the AIC does not reach a local minimum
within this range when using firstAICmin = TRUE, the function
stops with an error. Increase maxLag if this occurs.
logical flag. If TRUE the final
AR order is selected using the first local AIC minimum; otherwise
the order is selected by the overall minimum across all lags up to
maxLag. See Details.
logical flag. If TRUE the function
prints information from the AR modeling to the screen.
a character vector to determine the AR
model fitting. See details below. Possible values are either
"ar.yw" or "arima.CSS-ML". Can be abbreviated.
Defaults to "ar.yw".
Andy Bunn with contributions from Kevin Achukaitis and Ed Cook. Much of the function is a port of Cook's FORTRAN code.
This produces three mean-value chronologies: standard, residual, and ARSTAN. Users unfamiliar with the concept behind the ARSTAN method should look to Cook (1985) for background and inspiration.
The standard chronology is the (biweight) mean value across rows and
identical to chron.
The residual chronology is the prewhitened chronology as described by
Cook (1985) and uses multivariate autoregressive modeling to determine
the order of the AR process. It is important to note that the residual
chronology produced here is different from the simple residual
chronology produced by chron, which returns the
residuals of an AR process using a naive call to ar. In
practice the results will be similar. For more on the residual
chronology in this function, see pp. 153-154 in Cook's 1985
dissertation.
The ARSTAN chronology builds on the residual chronology but returns a re-whitened chronology where the pooled AR coefficients from the multivariate autoregressive modeling are reintroduced. See references for details.
The order of the AR model is selected from the pooled AR coefficients
by AIC using either the first local AIC minimum
(firstAICmin = TRUE, the default) or the overall minimum across
all lags up to maxLag (firstAICmin = FALSE). When
firstAICmin = TRUE and the AIC decreases monotonically across
all tested lags without reaching a local minimum, the function stops
with an error. This can occur when maxLag is too small for the
data or when the series have persistence structures that are not
well-suited to this approach (e.g., non-stationary or very long-memory
series). In such cases, consider increasing maxLag or reviewing
the data preparation steps described in Cook (1985). When
firstAICmin = FALSE the function always selects an order and
does not stop in this way.
If the selected AR order is zero (no detectable common autocorrelation among the series), no prewhitening or post-reddening is applied and all three returned chronologies are identical to the standard chronology.
Once the AR order is determined an AR(p) model is fit to each series
using either ar via the Yule-Walker method or by
arima via conditional-sum-of-squares to find starting
values, then maximum likelihood. It is possible that the model will
not converge in which case a warning is produced. The AR fitting is
determined via prewhitenMethod and defaults to using
ar.
Cook, E. R. and Kairiukstis, L. A., editors (1990) Methods of Dendrochronology: Applications in the Environmental Sciences. Springer. ISBN-13: 978-0-7923-0586-6.
Cook, E. R. (1985). A Time Series Analysis Approach to Tree Ring Standardization. PhD thesis, The University of Arizona.
library(graphics)
library(utils)
data(co021)
co021.rwi <- detrend(rwl = co021, method = "AgeDepSpline")
co021.crn <- chron.ars(co021.rwi)
plot(co021.crn,xlab="Year",ylab="RWI",add.spline=TRUE,nyrs=20)
cor(co021.crn)
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