Description Details Note Author(s) References

'RolWinMulCor' estimates the rolling (running) window correlation for the bi- and multi-variate cases between regular (sampled on identical time points) time series, with especial emphasis to ecological data although this can be applied to other kinds of data sets. 'RolWinMulCor' is based on the concept of rolling, running, or sliding window correlation and is useful to evaluate the evolution of correlation through time and time-scales. 'RolWinMulCor' contains six (four for estimations and two for plots) functions. The first two functions focus on the bi-variate case: (1) 'rolwincor_1win' and (2) 'rolwincor_heatmap', which estimate the correlation coefficients and their respective p-values for only one window-length (time-scale) and considering all possible window-lengths or a band of window-lengths, respectively. The second two functions: (3) 'rolwinmulcor_1win' and (4) 'rolwinmulcor_heatmap' are designed to analyze the multi-variate case, following the bi-variate case to visually display the results, but these two approaches are methodologically different. That is, the multi-variate case estimate the adjusted coefficients of determination instead of the correlation coefficients. The last two functions: (5) 'plot_1win' and (6) 'plot_heatmap' are used to plot the time series under study and to represent graphically the outputs of the four aforementioned functions as simple plots or as heat maps. The six functions contained in 'RolWinMulCor' are highly flexible since these contain several parameters to control the estimation of correlation and the features of the plot output, e.g. to remove the linear trend contained in the time series under analysis, to choose different p-value correction methods (which are used to address the multiple comparison problem) or to personalise the plot output. The 'RolWinMulCor' package also provides examples with synthetic and real-life ecological time series to exemplify its use.

Package: | RolWinMulCor |

Type: | Package |

Version: | 1.2 |

Date: | 2020-04-13 |

License: | GPL (>= 2) |

LazyLoad: | yes |

RolWinMulCor package contains six functions: (1) `rolwincor_1win`

estimates the rolling window correlation coefficients and their respective p-values for the bi-variate case for only one window-length or time-scale for the time series under study; (2) `rolwincor_heatmap`

estimates the correlation coefficients and their corresponding p-values taking into account all the possible window-lengths that are determined by the number of elements of the time series under analysis or a band of window-lengths; (3) `rolwinmulcor_1win`

estimates the rolling window correlation coefficients and their p-values for the multi-variate case for only one window-length or time-scale for the time series under study; (4) `rolwinmulcor_heatmap`

estimates the correlation coefficients and their corresponding p-values for the multi-variate case taking into account all the possible window-lengths or a band of window-lengths; (5) `plot_1win`

plots the time times under analysis and the correlation coefficients and their respective p-values (corrected or not corrected) as only one selected window-length using the outputs of the functions `rolwincor_1win`

(bi-variate case) and `rolwinmulcor_1win`

(multi-variate case); and (6) `plot_heatmap`

plots the time series under scrutiny and the heat map for the correlation coefficients and their respective p-values (corrected or not corrected) for all possible window-lengths (i.e., from five to the number of elements of the time series under analysis) or for a band of window-lengths using the outputs of the functions `rolwincor_heatmap`

(bi-variate case) and `rolwinmulcor_heatmap`

(multi-variate case). The bi-variate case follow from a methodological point of view to Telford (2013), Polanco-Martínez (2019), and Polanco-Martínez (2020) whereas the multi-variate case follow to Abdi (2007) and Polanco-Martínez (2020).

Dependencies: *stat*, *gtools*, *zoo*, *pracma* and *colorspace*.

Josué M. Polanco-Martínez (a.k.a. jomopo).

BC3 - Basque Centre for Climate Change, Bilbao, SPAIN.

Web1: https://scholar.google.es/citations?user=8djLIhcAAAAJ&hl=en.

Web2: https://www.researchgate.net/profile/Josue-Polanco-Martinez.

Email: josue.m.polanco@gmail.com, josue.polanco@bc3research.org.

Acknowledgement:

The author acknowledges to the SEPE (Spanish Public Service of Employment) for its funding support. Special thanks to the CRAN team (in particular to Martina Schmirl and Jelena Saf), to Ana-Maria Hereş and Jorge Curie for their helpful comments on the package, and for the three reviewers (this package is described in the paper recently published in *Ecological Informatics* and that is cited in the References section), in particular Reviewer #2, that provided very useful suggestions to improve RolWinMulCor.

Abdi H. Multiple correlation coefficient, in Encyclopedia of Measurement and
Statistics, N. J. Salkind, Ed. Sage, Thousand Oaks, CA, USA, 2007; 648-651.

<URL: https://personal.utdallas.edu/~herve/Abdi-MCC2007-pretty.pdf>.

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: doi: 10.1111/j.2517-6161.1995.tb02031.x>.

Polanco-Martínez, J. M. (2019). Dynamic relationship analysis between NAFTA stock markets using nonlinear, nonparametric, non-stationary methods. Nonlinear Dynamics, 97(1), 369-389. <URL: doi: 10.1007/s11071-019-04974-y>.

Polanco-Martínez, J. M. (2020). RolWinMulCor: an R package for estimating rolling window multiple correlation in ecological time series. Ecological Informatics, 60, 101163. <URL: doi: 10.1016/j.ecoinf.2020.101163>.

Telford, R.: Running correlations – running into problems (2013). <URL:

https://quantpalaeo.wordpress.com/2013/01/04/>.

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