Package {mqqr}

mqqr: Multivariate Quantile-on-Quantile Regression

Description

Implements the multivariate Quantile-on-Quantile regression of Sinha et al. (2023) extending the bivariate QQR of Sim and Zhou (2015) with exogenous moderators and optional interaction terms.

Main functions

• mqq_regression – the multivariate QQR estimator.

• plot_mqq_3d, plot_mqq_heatmap, plot_mqq_contour, plot_mqq_interaction – visualisations.

• mqq_to_matrix, mqq_export, mqq_statistics – helpers.

• parula_colors, mqqr_colorscales – colour palettes.

Author(s)

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

Multivariate Quantile-on-Quantile Regression

Description

Fits a multivariate Quantile-on-Quantile regression with optional moderators and interaction terms.

Usage

mqq_regression(y, x, moderators = list(),
               y_quantiles = seq(0.05, 0.95, by = 0.05),
               x_quantiles = seq(0.05, 0.95, by = 0.05),
               bandwidth = 0.05, include_lag = TRUE,
               interactions = TRUE, se = c("bootstrap", "none"),
               n_boot = 200, cdf_based_kernel = TRUE,
               x_name = "X", y_name = "Y",
               verbose = TRUE, seed = 42)

Arguments

Value

An object of class mqq_regression.

References

Sinha, A., Ghosh, V., Hussain, N., Nguyen, D.K., Das, N. (2023). Energy Economics, 126, 107021.

Sim, N., Zhou, H. (2015). Journal of Banking and Finance, 55, 1-12.

Examples

set.seed(1); n <- 200
x <- rnorm(n); z <- rnorm(n)
y <- 0.3*x + 0.2*z + 0.1*x*z + rnorm(n, sd=0.4)
fit <- mqq_regression(y, x, list(Z = z), n_boot = 30, verbose = FALSE)
print(fit)

Helpers for m-QQR results

Description

Pivot, export and summarise m-QQR results.

Usage

mqq_to_matrix(mqq_result, value = "beta1", moderator = NULL)
mqq_export(mqq_result, prefix, digits = 4)
mqq_statistics(mqq_result, alpha = 0.05)

Arguments

Value

Matrix, NULL, or data frame.

Examples

set.seed(1); n <- 60
x <- rnorm(n); z <- rnorm(n)
y <- 0.3 * x + 0.2 * z + rnorm(n, sd = 0.4)
fit <- mqq_regression(y, x, list(Z = z),
                      y_quantiles = c(0.25, 0.5, 0.75),
                      x_quantiles = c(0.25, 0.5, 0.75),
                      n_boot = 5, verbose = FALSE)
M <- mqq_to_matrix(fit, "beta1")
mqq_statistics(fit)
mqq_export(fit, file.path(tempdir(), "mqq"))

MATLAB-style and Sinha-paper colour palettes

Description

Colour palettes used by mqqr plotting functions. The default colour scale across all mqqr 3D and heatmap functions is MATLAB Parula (R2014b default), reproduced exactly from MathWorks' RGB stops.

Usage

parula_colors(n = 256)
matlab_jet_colors(n = 256)
turbo_colors(n = 256)
bluered_colors(n = 256)
sinha_colors(n = 256)
mqqr_palette(cols, n_breaks = 32)
resolve_colorscale(name = "Parula", n_breaks = 32)
mqqr_colorscales(show_preview = TRUE)

Arguments

Value

Character vector or list, depending on the function.

Examples

parula_colors(8)
matlab_jet_colors(8)
turbo_colors(8)
bluered_colors(8)
sinha_colors(8)
mqqr_colorscales(show_preview = FALSE)

Visualisations for m-QQR Results

Description

3D surface, heatmap, contour and moderator-interaction plots for results of mqq_regression, defaulting to MATLAB Parula.

Usage

plot_mqq_3d(mqq_result, value = "beta1", moderator = NULL,
            colorscale = "Parula", show_contour = TRUE,
            x_label = "X Quantile (tau)",
            y_label = "Y Quantile (theta)",
            title = NULL)

plot_mqq_heatmap(mqq_result, value = "beta1", moderator = NULL,
                 colorscale = "Parula",
                 x_label = "X Quantile (tau)",
                 y_label = "Y Quantile (theta)",
                 title = NULL, show_stars = FALSE)

plot_mqq_contour(mqq_result, value = "beta1", moderator = NULL,
                 colorscale = "Parula",
                 x_label = "X Quantile (tau)",
                 y_label = "Y Quantile (theta)",
                 title = NULL)

plot_mqq_interaction(mqq_result, moderator,
                     value = c("gamma", "alpha"),
                     colorscale = "Parula",
                     kind = c("3d", "heatmap", "contour"), ...)

Arguments

Value

A plotly object.

Examples

## Small toy example -- auto-tested. Plot objects are constructed but
## not rendered when run non-interactively.
set.seed(1); n <- 60
x <- rnorm(n); z <- rnorm(n)
y <- 0.4 * x + 0.2 * z + rnorm(n, sd = 0.4)
fit <- mqq_regression(y, x, list(Z = z),
                      y_quantiles = c(0.25, 0.5, 0.75),
                      x_quantiles = c(0.25, 0.5, 0.75),
                      n_boot = 5, verbose = FALSE)
p1 <- plot_mqq_3d(fit, colorscale = "Parula")
p2 <- plot_mqq_heatmap(fit, value = "beta1", show_stars = TRUE)
p3 <- plot_mqq_contour(fit, value = "beta1")
p4 <- plot_mqq_interaction(fit, "Z", value = "gamma", kind = "heatmap")

Numerical building blocks for QQ regression

Description

Low-level utilities exposed for advanced users: Gaussian kernel weights on the empirical-CDF scale, and weighted quantile regression via quantreg::rq.wfit.

Usage

qq_weights(x, tau, h = 0.05, cdf_based = TRUE)
gaussian_kernel(u)
weighted_qr(y, X, tau, weights = NULL)

Arguments

Value

Numeric vector (qq_weights, gaussian_kernel) or list (weighted_qr).

Examples

set.seed(1)
x <- rnorm(100)
w <- qq_weights(x, tau = 0.3)
sum(w)            # weights sum to length(x)
k <- gaussian_kernel(seq(-3, 3, by = 1))
X <- cbind(1, x)
y <- 0.5 * x + rnorm(100, sd = 0.3)
fit <- weighted_qr(y, X, tau = 0.5, weights = w)
fit$coef