The rolwincor_heatmap function estimates the rolling (running) window correlation between TWO time series (bi-variate case) sampled on identical time points for all the possible (i.e. from 3 to the number of elements of the time series under analysis) window-lengths or for a band of window-lengths and plots the correlation coefficients and their respective p-values (<= 0.05) as a heat map. To carry out the computational implementation we extend the works of Telford (2013) and Polanco-Mart<U+00ED>nez (2019). The rolwincor_heatmap function is highly flexible since this contains a great number of parameters to control the estimation of correlation and features of the plot output. A list of parameters are described in the following lines.
rolwincor_heatmap(inputdata, varnametsX="", varnametsY="", units="",
coltsX="black", coltsY="blue", CEXLAB=1.15, CEXAXIS=1.5,
LWDtsX=1, LWDtsY=1, CorMethod="spearman", typewidthwin="FULL",
widthwin_1=3, widthwin_N=dim(inputdata)[1],
Align="center", pvalcorectmethod="BH", rmltrd="Y",
Scale="Y", device="screen", Hfig=900, Wfig=900,
resfig=150, Hpdf=7, Wpdf=7, NUMLABX=5, ofilename)Matrix of 3 columns: time, first variable (e.g. \(X\)), and second variable (e.g. \(Y\)).
Names of the first (e.g. \(X\)) and second (e.g. \(Y\)) variable. Please note that the names of these two variables MUST be defined.
Time's unit (e.g. days, weeks, years, etc.) for the variables under analysis. Please note that the units MUST be defined.
The colors to be used to plot the two variables under study, by default the colors are ``black'' and ``blue,'' respectively, but it is possible to use other colors.
These parameters are used to plot the sizes of X-axis and Y-axis labels and X- and Y-axis, by default these parameters have values of 1.15 and 1.5, respectively, but it is possible to use other values.
These parameters are used to define the line-widths when the variables are plotted, by default these have values of 1, but other values (widths) can be used.
The method used to estimate the correlations, by default is ``spearman'' but other options (``pearson'' and ``kendall'') are available (please look at: R>?cor.test).
There are two options to estimate the rolling correlations and to plot the heat map: (1) typewidthwin=``PARTIAL'' to plot a band of windows from widthwin_1 to widthwin_N (both parameters were previously defined), or (2) typewidthwin=``FULL'' to plot all the possible window-lengths (from 3 to dim(inputdata)[1]), by default is FULL.
First value for the size (length) of the windows when the option typewidthwin=``PARTIAL'' is selected, the minimum value is 3 (the default value), but you should define this parameter (please note that widthwin_1 < widthwin_N).
Last value for the size (length) of the windows when the option typewidthwin=``PARTIAL'' is selected, by default is dim(inputdata)[1], but you should define this parameter (please note that widthwin_1 < widthwin_N).
To align the rolling object, RolWinMulCor ONLY uses the ``center'' option (please look at: R>?running) to ensure that variations in the correlation are aligned with the variations in the relationship of the time series under study rather than being shifted (Polanco-Mart<U+00ED>nez 2019).
The p-value correction method to be used, by default the method of Benjamini and Hochberg (BH) (1995) is used since this is less conservative and performs much better than Bonferroni, but other six methods (e.g. Holm, Bonferroni, etc.) are available (please look at: R>?p.adjust).
Remove (by default is ``Y'' or ``y''; please use ``N'' or ``n'' otherwise) the linear trend in the time series under analysis.
Scale (by default is ``Y'' or ``y''; please use ``N'' or ``n'' otherwise) is used to ``normalize'' or ``standardize'' the time series under analysis.
Kind of plot output (please look at: R>?device), there are five options: ``png'', ``jpeg/jpg'', ``eps'', ``pdf'' and ``screen.'' By default device is ``screen.''
Plot's height and width (for the device) for ``png'' and ``jpg'' format (look at R>?png or R>?jpg), by default Hfig and Wfig have values of 900, but other values can be used.
Image resolution (in ``ppi'') for the plot in ``png'' and ``jpg'' format (look at R>?png , R>?jpg or R>?jpeg), by default this has a value of 150, but other image resolutions can be used.
Plot's height and width (for the device) for ``pdf'' or ``eps'' format (>R?pdf or >R?postscript), by default Hpdf and Wpdf are equal to 7, but other values can be used.
Number of labels for (all) the X's axis, by the default is 5, but other number of labels can be utilized.
Output file name.
Outputs:
Plot output (heat map): screen or 'heatmap_bivariate_' + 'ofilename + .png, .jpg, .eps or .pdf'.
Numerical output: two lists matcor and pvalscor containing the correlation matrix and their corresponding corrected p-values, NoWindows and Windows that contains the number of windows and the window-lengths.
The rolwincor_heatmap function estimates the rolling window correlation between TWO time series (bi-variate case) sampled on identical time points for all the possible (i.e. from 3 to the number of elements of the time series under analysis) window-lengths or for a band of window-lengths and plots the rolling correlation coefficients and their respective p-values as a heat map. rolwincor_heatmap uses the functions running (package:gtools), the native R functions cor, cor.test, and p.adjust (package:stats), and some pieces of code written specifically to our R RolWinMulCor package.
Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B, 57 (1), 289-300. <URL: https://rss.onlinelibrary.wiley.com/doi/10.1111/j.2517-6161.1995.tb02031.x>.
Polanco-Mart<U+00ED>nez, J. M. (2019). Dynamic relationship analysis between NAFTA stock markets using nonlinear, nonparametric, non-stationary methods. Nonlinear Dynamics, 97(1), 369-389. <URL: https://doi.org/10.1007/s11071-019-04974-y>.
Telford, R.: Running correlations -- running into problems (2013). <URL: https://quantpalaeo.wordpress.com/2013/01/04/running-correlations-running-into-problems/>.
# NOT RUN {
# Loading packages
library("RolWinMulCor")
library("gtools")
library("pracma")
# Loading data set
data(synthetic_data)
# Testing the function rolwincor_heatmap
# typewidthwin="PARTIAL," window lengths from 21 to 31 and plot output in screen format
test1_rolwincor_heatmap <- rolwincor_heatmap(synthetic_data[,1:3], varnametsX="X",
varnametsY="Y", units="NU", typewidthwin="PARTIAL",
widthwin_1=21, widthwin_N=31, device="screen",)
# This example could takes a long time!
# typewidthwin="FULL" and pot output in PDF format
# }
# NOT RUN {
test2_rolwincor_heatmap <- rolwincor_heatmap(synthetic_data[,1:3], varnametsX="X",
varnametsY="Y", units="NU", typewidthwin="FULL",
device="pdf", ofilename="test2")
# }
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