Package {wqrr}

wqrr: Wavelet Quantile Regression Toolbox

Description

Eight wavelet-quantile estimators in one consistent interface: Wavelet Quantile Regression, Multivariate WQR, Wavelet Quantile-on-Quantile Regression with p-values, nonparametric Causality-in-Quantiles and its wavelet variant, Wavelet Quantile Mediation and Moderation, Wavelet Quantile Correlation, and a wavelet nonparametric Quantile Density estimator.

Main functions

• wavelet_qr - Wavelet Quantile Regression.

• multivariate_wqr - Multivariate WQR.

• wavelet_qqr - Wavelet QQR with p-values.

• np_quantile_causality - Causality-in-Quantiles.

• wavelet_np_causality - Wavelet variant.

• wavelet_mediation - Mediation / moderation.

• wavelet_quantile_correlation - WQC.

• wavelet_quantile_density - Quantile density.

• parula_colors, wqrr_colorscales - MATLAB-style colour palettes.

See also

For plain Quantile-on-Quantile regression see the companion CRAN package QuantileOnQuantile.

Author(s)

Dr Merwan Roudane merwanroudane920@gmail.com
GitHub: https://github.com/merwanroudane/wqrr

MODWT decomposition and band aggregation

Description

Maximal Overlap Discrete Wavelet Transform (MODWT) MRA via waveslim::mra, plus a helper to combine details into Short / Medium / Long bands.

Usage

modwt_mra(x, wavelet = "la8", level = NULL, boundary = "periodic")
aggregate_bands(details, band_spec = NULL)

Arguments

Value

For modwt_mra: a list with elements details and smooth. For aggregate_bands: a named list of aggregated band series.

Examples

set.seed(1); x <- cumsum(rnorm(128))
dec <- modwt_mra(x, "la8", level = 4)
bands <- aggregate_bands(dec$details)
sapply(bands, length)

Multivariate Wavelet Quantile Regression (MWQR)

Description

MWQR aggregates MODWT details into Short / Medium / Long bands and runs a multiple quantile regression of y_b on all regressors at each quantile within each band.

Usage

multivariate_wqr(y, X_list,
                 quantiles = c(0.05, 0.10, 0.25, 0.50,
                               0.75, 0.90, 0.95),
                 wavelet = "la8", J = 5, bands = TRUE,
                 dep_name = "Y", verbose = TRUE)

Arguments

Value

An object of class "mwqr_result".

Examples

set.seed(1); n <- 200
x1 <- cumsum(rnorm(n)); x2 <- cumsum(rnorm(n))
y  <- 0.4 * x1 - 0.2 * x2 + rnorm(n, sd = 0.5)
fit <- multivariate_wqr(y, list(X1 = x1, X2 = x2),
                        quantiles = c(0.25, 0.5, 0.75),
                        wavelet = "la8", J = 4, verbose = FALSE)

Nonparametric Causality-in-Quantiles (and Wavelet Variant)

Description

Nonparametric quantile Granger-causality test. Standard critical values are 1.96 (5%) and 1.645 (10%).

Usage

np_quantile_causality(x, y,
                      test_type = c("mean", "variance"),
                      q = seq(0.05, 0.95, by = 0.05),
                      bandwidth = NULL)

wavelet_np_causality(x, y,
                     test_type = c("mean", "variance"),
                     q = seq(0.05, 0.95, by = 0.05),
                     wavelet = "la8", J = 5,
                     bands = TRUE, bandwidth = NULL,
                     verbose = TRUE)

Arguments

Value

An object of class "causality_result" or "wavelet_causality_result".

References

Balcilar, M., Gupta, R., Pierdzioch, C. (2016). <doi:10.1016/j.resourpol.2016.04.004>.

Examples

set.seed(1); n <- 200
x <- rnorm(n); y <- 0.3 * c(0, x[-n]) + rnorm(n, sd = 0.5)
fit <- np_quantile_causality(x, y, q = c(0.25, 0.5, 0.75))

MATLAB-style colour palettes for wqrr

Description

Colour palettes used by wqrr plots, with MATLAB Parula as the default. The Parula stops are reproduced exactly from MathWorks' 64 RGB values.

Usage

parula_colors(n = 256)
matlab_jet_colors(n = 256)
turbo_colors(n = 256)
bluered_colors(n = 256)
sinha_colors(n = 256)
green_orange_red_colors(n = 256)
green_yellow_red_colors(n = 256)
wqrr_palette(cols, n_breaks = 32)
resolve_colorscale(name = "Parula", n_breaks = 32)
wqrr_colorscales(show_preview = TRUE)

Arguments

Value

Character vector or plotly colorscale list, depending on the function.

Examples

parula_colors(8)
wqrr_colorscales(show_preview = FALSE)

Visualisations for wqrr Results

Description

Interactive 3D surfaces, heatmaps and contour plots for all wqrr estimators. All default to the MATLAB 'Parula' colour map (see parula_colors and wqrr_colorscales).

Usage

plot_qq_3d(qq_result, value = "coefficient",
           colorscale = "Parula", show_contour = TRUE,
           x_label = "X Quantile (tau)",
           y_label = "Y Quantile (theta)", title = NULL)

plot_qq_heatmap(qq_result, value = "coefficient",
                colorscale = "Parula", show_stars = FALSE,
                x_label = "X Quantile (tau)",
                y_label = "Y Quantile (theta)", title = NULL)

plot_qq_contour(qq_result, value = "coefficient",
                colorscale = "Parula",
                x_label = "X Quantile (tau)",
                y_label = "Y Quantile (theta)", title = NULL)

plot_wqr_heatmap(wqr_result, value = "beta",
                 colorscale = "GreenOrangeRed",
                 title = "Wavelet Quantile Regression",
                 x_label = "Quantiles",
                 y_label = "Time Horizons")

plot_wqqr_surface(wqqr_result, colorscale = "Parula", title = NULL)

plot_wqqr_pvalue_heatmap(wqqr_result, alpha = 0.05,
                         colorscale = "Sinha", title = NULL)

plot_wqr_vs_wqqr(wqqr_result, ...)

plot_causality(causality_result, cv = 1.96, title = NULL)

plot_wavelet_causality(wcr, colorscale = "GreenOrangeRed", title = NULL)

plot_correlation_heatmap(x, y,
                         quantiles = seq(0.1, 0.9, by = 0.1),
                         colorscale = "RdBu",
                         title = "Quantile Correlation Heatmap")

plot_wqc_heatmap(wqc_result, colorscale = "Parula",
                 title = "Wavelet Quantile Correlation")

plot_quantile_density(qd_result, ...)

plot_mediation_panel(med_result, colorscale = "GreenYellowRed")

Arguments

Value

A plotly object (or a named list of plotly objects for plot_mediation_panel).

Examples

set.seed(1); n <- 128
x <- cumsum(rnorm(n)); y <- 0.5 * x + rnorm(n, sd = 0.5)
fit <- wavelet_qr(y, x, quantiles = c(0.25, 0.5, 0.75),
                  wavelet = "la8", J = 4, verbose = FALSE)
p <- plot_wqr_heatmap(fit, colorscale = "Parula")

Formatted coefficient table with significance stars

Description

Convenience formatter to insert WQR / MWQR / mediation slope coefficients into a paper-style table.

Usage

results_table(x, value = "beta", digits = 3,
              row = "level", variable = NULL)

Arguments

Value

Character data frame with rows = bands and columns = quantiles. Entries look like "0.345**" (stars for 1% / 5% / 10%).

Examples

set.seed(1); n <- 128
x <- cumsum(rnorm(n)); y <- 0.5 * x + rnorm(n, sd = 0.5)
fit <- wavelet_qr(y, x, quantiles = c(0.25, 0.5, 0.75),
                  wavelet = "la8", J = 4, verbose = FALSE)
results_table(fit)

Wavelet Quantile Mediation and Moderation

Description

Five wavelet-band quantile regressions for the triplet (y, x, z): direct effect, x*z moderation (interaction), path a (x -> z), path b (z -> y | x), indirect (a * b).

Usage

wavelet_mediation(y, x, z,
                  quantiles = c(0.05, 0.10, 0.25, 0.50,
                                0.75, 0.90, 0.95),
                  wavelet = "la8", J = NULL,
                  dep_name = "Y", main_name = "X",
                  mod_name = "Z", verbose = TRUE)

Arguments

Value

An object of class "mediation_result" containing five data frames: direct, interaction, path_a, path_b, indirect.

Examples

set.seed(1); n <- 200
x <- rnorm(n); z <- 0.4 * x + rnorm(n, sd = 0.5)
y <- 0.3 * x + 0.4 * z + rnorm(n, sd = 0.5)
fit <- wavelet_mediation(y, x, z,
                         quantiles = c(0.25, 0.5, 0.75),
                         wavelet = "la8", J = 4, verbose = FALSE)

Wavelet Quantile-on-Quantile Regression with p-values (WQQR)

Description

For a selected MODWT frequency band, builds the (theta, tau) coefficient and p-value surface of a kernel-weighted local linear quantile regression of y_b on x_b. Also returns the standard band-level WQR slopes for comparison.

Usage

wavelet_qqr(y, x, quantile_step = 0.05,
            wavelet = "la8", J = 5,
            band = "long", bandwidth = 1.0,
            verbose = TRUE)

Arguments

Value

An object of class "wqqr_result" with coefficient matrix, p-value matrix, the standard WQR slopes (qr_coef) and their p-values.

Examples

set.seed(1); n <- 128
x <- cumsum(rnorm(n)); y <- 0.4 * x + rnorm(n, sd = 0.5)
fit <- wavelet_qqr(y, x, quantile_step = 0.25,
                   wavelet = "la8", J = 4, band = "long",
                   verbose = FALSE)

Wavelet Quantile Regression (WQR)

Description

Decompose y and x by MODWT, then run quantile regression of y_b on x_b at each quantile in each band b.

Usage

wavelet_qr(y, x,
           quantiles = seq(0.05, 0.95, by = 0.05),
           wavelet = "la8", J = 5,
           bands = TRUE, verbose = TRUE)

wqr_to_matrix(wqr, value = "beta")

Arguments

Value

An object of class "wqr_result" (or numeric matrix).

References

Adebayo, T.S., Ozkan, O. (2024) <doi:10.1016/j.jclepro.2024.140832>.

Examples

set.seed(1); n <- 128
x <- cumsum(rnorm(n)); y <- 0.5 * x + rnorm(n, sd = 0.5)
fit <- wavelet_qr(y, x, quantiles = c(0.25, 0.5, 0.75),
                  wavelet = "la8", J = 4, verbose = FALSE)
wqr_to_matrix(fit)

Wavelet Quantile Correlation (WQC)

Description

Quantile correlation between MODWT detail series of two time series, with parametric-bootstrap 95% confidence intervals.

Usage

wavelet_quantile_correlation(x, y,
                             quantiles = c(0.05, 0.25, 0.50,
                                           0.75, 0.95),
                             wavelet = "la8", J = 8,
                             n_sim = 200, verbose = TRUE)

Arguments

Value

An object of class "wqc_result".

Examples

set.seed(1); n <- 256
x <- cumsum(rnorm(n)); y <- 0.4 * x + rnorm(n, sd = 0.5)
fit <- wavelet_quantile_correlation(
  x, y, quantiles = c(0.25, 0.5, 0.75),
  J = 4, n_sim = 20, verbose = FALSE)

Wavelet Quantile Density Estimation

Description

Three nonparametric estimators of the quantile density q(p) = 1 / f(F^-1(p)): linear wavelet, hard-thresholded, and local-linear smoothed.

Usage

wavelet_quantile_density(y, j0 = 5, bandwidth = 0.15,
                         wavelet = "haar",
                         gld_params = NULL)

Arguments

Value

An object of class "quantile_density_result".

Examples

set.seed(1); y <- rnorm(256)
qd <- wavelet_quantile_density(y, j0 = 4)