Bubble Contagion Regression (Greenaway-McGrevy & Phillips 2016)

contagion_reg estimates the time-varying contagion coefficient of Greenaway-McGrevy & Phillips (2016): a fixed-window rolling AR(1) coefficient sequence for a "core" series and a "satellite" series y, related by a functional (Nadaraya-Watson kernel) regression at a chosen delay d – how strongly and how (time-varying) does the core series' local persistence transmit to y, d periods later.

Usage

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

# S3 method for class 'contagion_reg_obj'
autoplot(object, ...)

Arguments

y: Satellite (dependent) series, numeric vector.
core: Core (reference) series, numeric vector, same length as y.
S: Fixed rolling-window width for the AR(1) coefficient sequence (default floor(0.33 * length(y)), the paper's own choice).
d: Non-negative integer delay (default 0).
h: Bandwidth for the Nadaraya-Watson regression. Default NULL selects it via 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)).
object: An object of class contagion_reg_obj, the output of contagion_reg.

Value

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

Details

This is the minimum-viable subset of the paper's own procedure: 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 (searching over d automatically) is not implemented – call contagion_reg once per candidate d and compare fit if an automatic search is needed.

The paper performs no formal inference (no confidence bands, no hypothesis test) on the contagion coefficient itself – this is a point-estimation and visualization tool, not a test, matching what the source paper itself does.

Note

Not a hypothesis test: contagion_reg performs no formal inference (no confidence bands, no significance test) on the contagion coefficient, so there is no critical value at all for this function – don't look for one.

Returns its own class (not radf_obj), so it does not plug into summary()/\link{datestamp}/tidy/autoplot – prints its own coefficient-path summary (it performs no formal inference at all) – see vignette("naming-and-analysis", package = "exuber") for the full picture of which functions do and don't fit that pipeline.

Status

References

Greenaway-McGrevy, R., & Phillips, P. C. B. (2016). Hot property in New Zealand: Empirical evidence of housing bubbles in the metropolitan centres. New Zealand Economic Papers, 50(1), 88-113.

Examples

# \donttest{
res <- contagion_reg(sim_data$psy1, sim_data$psy2, d = 0L)
print(res)
#> 
#> ── contagion_reg (n = 100, S = 33, d = 0, h = 0.6567) ──────────────────────────
#> 
#> delta_2(r) range: [0.163, 0.182] 
#> 

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


# Compare a one-period lead (d = 1) against the contemporaneous case
res_d1 <- contagion_reg(sim_data$psy1, sim_data$psy2, 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)

# }