NEWS
hatemicoint 1.1.0 (2026-10-01)
This release corrects the Phillips statistics and changes several defaults.
Results differ from version 1.0.1 for every data set.
- Zt statistic (R/utils.R): the statistic was multiplied by an extra factor
sqrt(n - 1). It is now Zt = (rho* - 1) / sqrt(sigma2 / sum_{t=1}^{n-1} u_t^2),
the form of Gregory and Hansen (1996, p. 105) and Phillips (1987); equation
(6) of Hatemi-J (2008) as printed omits the square root in the denominator. With
kernel = "iid"
Zt now equals the Dickey-Fuller t-ratio up to the residual-variance divisor
(n instead of n - 2); the old value was about ten times too large in
absolute value for n = 100.
- Serial-correlation correction: the correction subtracted from the
cross-product term was twice the one-sided sum sum_{j>=1} w(j/B) gamma(j)
of equation (3). It is now the one-sided sum, lambda = (sigma2 - gamma(0))/2,
multiplied by n to undo the 1/n in the autocovariances of equation (4), as
in Phillips (1987). Sums use the normalisation of the paper: sum over
t = 1, ..., n - 1 of u_t^2, autocovariances divided by n, and
Za = n (rho* - 1).
- Quadratic spectral kernel: the weight used z = 6 pi j / B instead of
z = 6 pi (j/B) / 5 (Andrews 1991), and the sum was truncated at the
bandwidth. The QS sum now runs over all lags with the correct weight. The
Bartlett weight changed from 1 - j/(B + 1) (Newey-West form, used in
1.0.1) to 1 - j/B, the kernel k(x) = 1 - |x| evaluated at x = j/B, matching
the paper's w(j/B) notation and the way the QS kernel is evaluated. This is
the package's choice, not a correction from the paper; results with
kernel = "bartlett" and a given bwl therefore differ from 1.0.1. With
integer B only lags 1, ..., B - 1 enter, so bwl = 1 gives no correction.
- New defaults for the Phillips statistics:
kernel = "qs" with AR(1)
prewhitening (new argument prewhite = TRUE) and, when bwl = NULL, the
Andrews (1991) automatic bandwidth for the QS kernel, following footnote 3
of the paper and Andrews and Monahan (1992). The AR(1) coefficient is capped
at 0.97 in absolute value and the kernel estimate is recoloured by
1/(1 - a1)^2. The bandwidth is chosen for every break pair; the values at
the selected break pairs are returned as bwl_zt and bwl_za. Versions
before 1.1.0 used kernel = "iid" (no correction) by default. For
kernel = "bartlett" with bwl = NULL the old rule
round(4 (n/100)^(2/9)) is kept.
- ADF lag selection: candidate lags are now compared on a common sample
(the first
maxlags usable observations are dropped for every candidate)
for the "tstat", "aic" and "sic" rules; the final statistic for the chosen
lag is computed on the largest sample available for that lag. The lag is
still re-selected for every break pair. New rule lag_selection = "fixed"
uses maxlags lags. The default maxlags is now
floor(4 (n/100)^(1/4)) (Schwert rule; the paper does not give a lag rule)
instead of 8. The selected lag at the ADF* break pair is returned as
lag_adf.
- Break grid: the bounds were rounded separately, so for some n (for example
24, 50, 57) pairs outside the trimming region were used. tb1 now runs from
ceiling(0.15 n) to floor(0.70 n) and tb2 from tb1 + ceiling(0.15 n) to
floor(0.85 n), so that tb1 >= 0.15 n, tb2 <= 0.85 n and tb2 - tb1 >= 0.15 n
for every n (the test suite checks every n from 20 to 2000).
- A singular regressor matrix in the ADF regression was replaced by a huge
diagonal (giving a statistic near zero) and the long-run variance was
floored at 1e-10. Both now give NA for that break pair, the pair is skipped
in the infimum and a warning reports the number of skipped pairs
(
n_skipped in the result). Missing values in y or x are an error.
print and summary show the prewhitening, the bandwidth and NA break
dates when no statistic could be computed.- Added a testthat suite pinning every statistic to hand computations and
checking the break grid bounds.
hatemicoint 1.0.0
Initial CRAN Release
- Implements the Hatemi-J (2008) cointegration test with two unknown regime shifts
- Three test statistics: ADF*, Zt*, and Za*
- Lag selection methods: t-statistic, AIC, SIC
- Kernel options: IID, Bartlett, Quadratic Spectral
- Critical values for k = 1 to 4 regressors
- Print and summary methods for test results
References
- 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