Bubble Contagion Regression (Greenaway-McGrevy & Phillips 2016)

contagion_reg(
  y,
  core,
  S = NULL,
  d = 0L,
  h = NULL,
  r_grid = seq(0, 1, length.out = 100)
)

contagion_reg estimates the time-varying contagion coefficient of Greenaway-McGrevy & Phillips (2016). It computes a fixed-window rolling AR(1) coefficient sequence for a "core" series and for a "satellite" series y and relates them with a functional (Nadaraya-Watson kernel) regression at a chosen delay d. The coefficient shows how strongly, and how it varies over time, the local persistence of the core series transmits to y, d periods later.

Arguments

y	Satellite (dependent) series, a numeric vector.
core	Core (reference) series, a numeric vector of the same length as y.
S	Fixed rolling-window width for the AR(1) coefficient sequence (default floor(0.33 * length(y)), the choice of the paper).
d	Non-negative integer delay (default 0).
h	Bandwidth for the Nadaraya-Watson regression. The default NULL selects it by leave-one-out cross-validation (eq. 7).
r_grid	Evaluation points for the time-varying coefficient, as fractions of the sample (default seq(0, 1, length.out = 100)).

Value

An object of class contagion_reg_obj: a list with the fixed-window AR(1) coefficient sequences (beta_core and beta_j), the selected or supplied bandwidth (h) and the estimated time-varying contagion coefficient (delta2, aligned with r_grid).

Details

This is a minimal subset of the procedure in the paper. It contains the fixed-window AR(1) coefficient sequence (their eq. 1), the Nadaraya-Watson regression at a single supplied d (eq. 6) and leave-one-out cross-validated bandwidth selection (eq. 7). Their eq. 8, the automatic search over d, is not implemented. If you need a search, call contagion_reg once for each candidate d and compare the fit.

The paper performs no formal inference on the contagion coefficient itself, with no confidence bands and no hypothesis test. As in the paper, this function is a tool for point estimation and visualization and not a test.

# A co-explosive pair: the AR coefficient of y follows that of x almost one for one
xy <- sim_coexplosive(n = 100, seed = 123)
res <- contagion_reg(xy$y, xy$x, d = 0L)
print(res)
#> 
#> ── contagion_reg (n = 100, S = 33, d = 0, h = 0.6567) ──────────────────────────
#> 
#> delta_2(r) range: [0.948, 0.965]

# Plot the estimated time-varying contagion coefficient
autoplot(res)

# Compare a one-period lead (d = 1) with the contemporaneous case
res_d1 <- contagion_reg(xy$y, xy$x, d = 1L)
autoplot(res) +
  ggplot2::geom_line(data = data.frame(r = res_d1$r_grid, delta2 = res_d1$delta2),
    ggplot2::aes(r, delta2), color = "red", inherit.aes = FALSE)