Estimate the Explosive Autoregressive Root over a Sub-Sample

Fits the no-intercept AR(1) regression \(y_t = \rho y_{t-1} + \epsilon_t\) over the sub-sample from:to of data – the model used by Phillips & Magdalinos (2007) and Guo, Sun & Wang (2019) for inference on a (moderately) explosive root, e.g. an episode already identified by datestamp. No intercept is included, following Phillips & Magdalinos's model (their eq. 58 excludes it "to exclude the presence of a deterministically explosive component").

Usage

explosive_root(data, from, to)

Arguments

data: A numeric vector (a single series).
from, to: Integer row positions delimiting the sub-sample (e.g. from datestamp()'s Start/End, converted to row positions if they are dates: match(start_date, index(x))).

Value

A list with rho (the OLS estimate), se (its standard error), t_stat, and n (sub-sample size).

Status

References

Phillips, P. C. B., & Magdalinos, T. (2007). Limit theory for moderate deviations from a unit root. Journal of Econometrics, 136(1), 115-130.