makicoint: Maki Cointegration Test with Multiple Structural Breaks

Overview

makicoint implements the Maki (2012) residual-based test for cointegration allowing for an unknown number of structural breaks. It extends the Gregory-Hansen (one break) and Hatemi-J (two breaks) tests to any feasible number of breaks, and is useful when the long-run relationship between non-stationary series may shift more than twice or is subject to regime changes.

Key features

• Any feasible number of breaks (not capped at five), bounded by the sample size and the trimming parameter.
• Four model specifications: level shift (0), level shift with trend (1), regime shift (2), and regime shift with trend (3).
• Two engines giving the same test statistic: the default reproduces the original GAUSS/tspdlib implementation; engine = "paper" uses the Maki (2012, Steps 2 and 4) break rule.
• Critical values from Maki (2012) Table 1 (depending on the number of regressors, breaks and model); simulated critical values for more than five breaks via simcv.
• Diagnostic plot (ggplot2): the series with its break-adjusted long-run fit, and the cointegrating residual.
• ADF lag rules: tsig (default), fixed, zero, aic, bic.

Installation

install.packages("makicoint")                       # CRAN
# devtools::install_github("merwanroudane/makicoint")  # development

Usage

library(makicoint)

set.seed(123)
n <- 100
x <- cumsum(rnorm(n))
y <- 0.5 * x + cumsum(rnorm(n))
y[51:100] <- y[51:100] + 2          # a level break at observation 50

res <- coint_maki(cbind(y, x), m = 1, model = 0)
res
plot(res)                           # requires ggplot2

Two breaks, regime-shift model, and the paper engine:

coint_maki(cbind(y, x), m = 2, model = 2)
coint_maki(cbind(y, x), m = 2, model = 2, engine = "paper")

Beyond five breaks, with simulated critical values (heavy):

coint_maki(cbind(y, x), m = 7, simcv = 2000, simt = 500)

Functions

• coint_maki() — the test.
• cv_coint_maki(k, m, model) — Maki (2012) Table 1 critical values.
• print() / plot() methods for the result.

Reference

Maki, D. (2012). Tests for cointegration allowing for an unknown number of breaks. Economic Modelling, 29, 2011-2015. doi:10.1016/j.econmod.2012.04.022

Author

Dr Merwan Roudane — Independent Researcher — merwanroudane920@gmail.com — github.com/merwanroudane

License

GPL-3