Find the Core (primary) group according to step 2 of the clustering algorithm by Phillips and Sul (2007, 2009)
coreG(X, dataCols, time_trim, threshold = -1.65, HACmethod = c("FQSB",
"AQSB"), type = c("max", "all"))matrix or dataframe containing data (preferably filtered data in order to remove business cycles)
integer vector with the column indices of the data
a numeric value between 0 and 1, representing the portion of time periods to trim when running log t regression model. Phillips and Sul (2007, 2009) suggest to discard the first third of the period.
numeric value indicating the threshold to be used to perform the one-tail t test; default is -1.65.
string indicating whether a Fixed Quadratic Spheric Bandwidth (HACmethod="FQSB") or
an Adaptive Quadratic Spheric Bandwidth (HACmethod="AQSB") should be used for the truncation
of the Quadratic Spectral kernel in estimating the log t regression model
with heteroskedasticity and autocorrelation consistent standard errors.
The default method is "FQSB".
one of "max" or "all"; "max" includes only the region with maximum t-value. The default option is "max"; "all" includes all regions that pass the test t in the core formation (step 2).
A numeric vector containing the row indices of the regions included
in the core group; if a core group cannot be found, returns FALSE.
According to the second step of the Phillips and Sul clustering algorithm (2007, 2009),
the log t regression should be run for the first k units \(2 < k < N\)
maximizing k under the condition that \(t-value > -1.65\).
In other words, the core group size \(k^*\) is chosen as follows:
$$ k^* = argmax_{k} \{t_k\} $$ subject to
$$\min{t_k} > -1.65$$
Such behavior is obtained with type="max"; if type="all",
all units that satisfy \(t_k > -1.65\) are added to core group.
If the condition \(t_k > -1.65\) does not hold for \(k = 2\) (the first two units), the algorithm drops the first unit and repeats the same procedure for the next pair of units. If \(t_k > -1.65\) does not hold for any couple of units, the whole panel diverges.
Phillips, P. C.; Sul, D., 2007. Transition modeling and econometric convergence tests. Econometrica 75 (6), 1771-1855.
Phillips, P. C.; Sul, D., 2009. Economic transition and growth. Journal of Applied Econometrics 24 (7), 1153-1185.