hatemicoint 1.1.0
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