hatemicoint implements the Hatemi-J (2008) cointegration test which allows for two unknown structural breaks (regime shifts) in the cointegrating relationship.
Standard cointegration tests may fail to detect cointegration when the relationship between variables has changed over time due to structural breaks. The Hatemi-J test addresses this by:
# Install from CRAN (when available)
install.packages("hatemicoint")
# Or install the development version from GitHub
# install.packages("devtools")library(hatemicoint)
# Generate example data with structural breaks
set.seed(123)
n <- 200
x <- cumsum(rnorm(n)) # I(1) regressor
# Create cointegrated series with two breaks
y <- numeric(n)
y[1:70] <- 1 + 0.8 * x[1:70] + rnorm(70, sd = 0.5)
y[71:140] <- 3 + 1.2 * x[71:140] + rnorm(70, sd = 0.5)
y[141:200] <- 2 + 0.6 * x[141:200] + rnorm(60, sd = 0.5)
# Run the Hatemi-J test
result <- hatemicoint(y, x)
print(result)
summary(result)The package computes three test statistics:
| Test | Description |
|---|---|
| ADF* | Augmented Dickey-Fuller test on residuals |
| Zt* | Phillips-Perron Z_t test |
| Za* | Phillips-Perron Z_α test |
All statistics test the null hypothesis of no cointegration against the alternative of cointegration with two structural breaks.
hatemicoint(y, x,
maxlags = NULL, # Max ADF lags; NULL = floor(4 * (n/100)^(1/4))
lag_selection = "tstat", # "tstat", "aic", "sic" or "fixed"
kernel = "qs", # "qs" (default), "bartlett" or "iid"
bwl = NULL, # Bandwidth; NULL = Andrews (1991) rule for "qs"
prewhite = TRUE, # AR(1) prewhitening (Andrews and Monahan 1992)
trimming = 0.15 # Trimming for break search
)The Phillips statistics follow equations (3) to (6) of Hatemi-J
(2008). By default the long-run variance is estimated with a prewhitened
quadratic spectral kernel and the Andrews (1991) automatic bandwidth, as
in footnote 3 of the paper. Versions before 1.1.0 used
kernel = "iid" and contained errors in the Zt statistic and
in the kernel correction; see NEWS.md.
Critical values from Hatemi-J (2008, Table 1):
| k | 1% | 5% | 10% |
|---|---|---|---|
| 1 | -6.503 | -6.015 | -5.653 |
| 2 | -6.928 | -6.458 | -6.224 |
| 3 | -7.833 | -7.352 | -7.118 |
| 4 | -8.353 | -7.903 | -7.705 |
| k | 1% | 5% | 10% |
|---|---|---|---|
| 1 | -90.794 | -76.003 | -52.232 |
| 2 | -99.458 | -83.644 | -76.806 |
| 3 | -118.577 | -104.860 | -97.749 |
| 4 | -140.135 | -123.870 | -116.169 |
Decision rule: Reject H₀ (no cointegration) if test statistic < critical value.
Hatemi-J, A. (2008). Tests for cointegration with two unknown regime shifts with an application to financial market integration. Empirical Economics, 35, 497-505. DOI: 10.1007/s00181-007-0175-9
Gregory, A.W. and Hansen, B.E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99-126. DOI: 10.1016/0304-4076(69)41685-7
GPL-3