This function calculates (potentially moving or evolving) response and correlation functions from tree-ring chronologies and monthly climatic data. For the moving case, the calculation is performed repeatedly for consecutive time windows. Function parameters may be bootstrapped to calculate their significance and confidence intervals.
dcc(
chrono,
climate,
selection = -6:9,
method = "response",
dynamic = "static",
moving,
win_size = 25,
win_offset = 1,
start_last = TRUE,
timespan = NULL,
var_names = NULL,
ci = 0.05,
boot = "stationary",
sb = TRUE,
verbose = TRUE
)'dcc' returns an 'object' of class '"tc_dcc"'.
The functions 'summary' and 'plot' are used to obtain and print a summary of the results, and to create a plot. The function 'coef' can be used to extract the coefficients.
An object of class '"tc_dcc"' is a list containing at least the following components:
the call made to function 'dcc'
the coefficients, themselves being an object of class 'tc_coef' for the static case, and of class 'tc_mcoef' for the moving case. Objects of class 'tc_coef' are single data.frames, while objects of class 'tc_mcoef' are lists of seperate data.frames for the coefficients (element 'coef'), upper and lower confidence interval (elements 'ci_upper' and 'ci_lower'), and significance flags (element 'significant')
the design matrix on which this call to 'dcc' operates
the input data truncated to the common timespan or the specified timespan
the original input data, with the climate data being recast into a single data.frame
data.frame containing a tree-ring
chronologies, e.g. as obtained by chron of package dplR.
either a data.frame or matrix with
climatic data in monthly resolution, with year, month and
climate parameters in columns (all columns except year and month
will be recognized as parameters for response or correlation
functions), or a single data.frame or matrix in
13-column format (see below), or a (potentially named) list of
one or several of the latter.
either a numeric vector, a modifier, or a chain of modifiers specifying the parameter selection for the model (see Details).
character string specifying the calculation
method. Possible values are “response” and
“correlation”. Partial strings are ok.
character; should the analyis be carried out
in a static, moving, or evolving fashion. One of
c("static", "moving", "evolving"). Defaults to
"static". Partial strings are ok.
deprecated, use dynamic instead.
integer giving the window size for each recalculation in years for a moving analysis, and the initial window size for an evolving analysis.
integer giving the number of years between each window start in years.
logical flag indicating whether the first
window should start at the rear end (youngest part of the
series) or not.
integer vector of length 2 specifying the
time interval (in years) to be considered for analysis. Defaults
to the maximum possible interval.
character vector with variable
names. Defaults to corresponding column names of parameter climate if
given as data.frame, or its names if given as list.
numerical value to set the test level for
significance test (values 0.01, 0.05 and 0.1 are allowed); the
confidence intervals are adapted accordingly.
character indicating which bootstrap method
should be used, one of c("stationary", "std", "exact")
logical flag indicating whether textual status
bar for moving case should be suppressed. Suppression is
recommended for e.g. Sweave files.
logical flag indicating if informative messages should
be written to the console (default is `TRUE`).
Christian Zang; the original MATLAB code for exact bootstrapping was written by Dave Meko
This function builds upon and extents the functionality of programme DENDROCLIM2002 (Biondi and Waikul, 2004), and will calculate bootstrapped (and non-bootstrapped) moving and static response and correlation functions in a similar fashion as described in the above mentioned paper. Important extensions include a very flexible parameter selection model (see below), the possibility to use an unlimited number of climate parameters, and the option to use exact bootstrapping.
Input chronology data can be a data.frame such as produced
by function chron of package dplR. It has to be a
data.frame with at least one column containing the
tree-ring indices, and the corresponding years as rownames.
For climatic input data, there are three possibilities: Firstly,
input climatic data can be a data.frame or matrix
consisting of at least 3 rows for years, months and at least one
climate parameter in the given order. Secondly, input climatic
data can be a single data.frame or matrix in the
style of the original DENDROCLIM2002 input data, i.e. one
parameter with 12 months in one row, where the first column
represents the year. Or thirdly, input climatic data can be a
(potentially named) list of one or several of the latter described
data.frame or matrices. If named list is provided,
potentially provided variable names through argument
var_names are ignored. As an internal format dispatcher
checks the format automatically, it is absolutely necessary that
in all three cases, only complete years (months 1-12) are
provided. It is not possible to mix different formats in one go.
Parameters can be selected with the 'selection' parameter in two different ways:
simple selections: as an example -6:9 selects from all
climate variables all months from previous year's June (-6,
previous year's months are specified as negative integers) to
current years September (9, months of the current year are
specified as positive integers) as model parameters. Months from
the previous year and the year before that can be selected using
treeclim-shifters like ..(6) to refer to July of
the year before the previous year.
using modifiers: More complex parameter selections
can be obtained by the modifiers provided in treeclim:
.range, .mean, and .sum. These modifiers
can also be chained to create complex selections. See
treeclim-modifiers for details.
For the exclusion of months, the convenience function
exclude_from (or short exfr) is
provided.
1000 bootstrap samples are taken from the original distributions
of climate and tree-ring data, either using the stationary
bootstrap (Politis and Romano 1994, boot = "stationary") or
classical bootstrap (DENDROCLIM2002-style, boot =
"std"). The stationary bootstrap mimics the stationary properties
of the original time series in the resampled time series by
resampling within blocks. Within each block, the number of
observations is random and has a geometric distribution.
Consequently, the choice of the distribution parameter will affect
the autocorrelation structure of the resampled time
series. Optimal (expected) block length is chosen according to
Politis and White (2004). In the case of response function
analysis, an eigen decomposition of the standardized predictor
matrix is performed. Nonrelevant eigenvectors are removed using
the PVP criterion (Guiot, 1990), principal component scores are
then calculated from the matrices of reduced eigenvectors and
standardized climatic predictors. Response coefficients are found
via singular value decomposition, and tested for significance
using the 95% percentile range method (Dixon, 2001). In case of
correlation function analysis, the coefficients are Pearson's
correlation coefficients. The same method for significance testing
is applied.
There is also the option to use exact bootstrapping like
implemented in seascorr (Meko et al. 2011, boot =
"exact"). In this case, circulant embedding is used to simulate
the tree-ring data 1000 times as time series with the same
frequency characteristics like the original time-series (Percival
& Constantine, 2006). Empirical non-exceedence probabilities are
used to test the coefficients of the response/correlation function
with the original data for significance. For the exact
bootstrapping case, no confidence intervals for the
response/correlation coefficients can be computed.
Biondi, F & Waikul, K (2004) DENDROCLIM2002: A C++ program for statistical calibration of climate signals in tree-ring chronologies. Computers & Geosciences 30:303-311
Dixon, PM (2001) Bootstrap resampling. In: El-Shaarawi, AH, Piegorsch, WW (Eds.), The Encyclopedia of Environmetrics. Wiley, New York.
Guiot, J (1991) The boostrapped response function. Tree-Ring Bulletin 51:39-41
Meko DM, Touchan R, Anchukaitis KJ (2011) Seascorr: A MATLAB program for identifying the seasonal climate signal in an annual tree-ring time series. Computers & Geosciences 37:1234-241
Percival DB, Constantine WLB (2006) Exact simulation of Gaussian Time Series from Nonparametric Spectral Estimates with Application to Bootstrapping. Statistics and Computing 16:25-35
Patton, A. and D.N. Politis and H. White (2009), "CORRECTION TO 'Automatic block-length selection for the dependent bootstrap' by D. Politis and H. White", Econometric Reviews 28(4), 372-375.
Politis, D.N. and H. White (2004), Automatic block-length selection for the dependent bootstrap, Econometric Reviews 23(1), 53-70.
dc_resp <- dcc(muc_spruce, muc_clim)
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