generalCorr - Generalized Correlations, Causal Paths and Portfolio Selection
Function gmcmtx0() computes a more reliable (general)
correlation matrix. Since causal paths from data are important
for all sciences, the package provides many sophisticated
functions. causeSummBlk() and causeSum2Blk() give
easy-to-interpret causal paths. Let Z denote control variables
and compare two flipped kernel regressions: X=f(Y, Z)+e1 and
Y=g(X, Z)+e2. Our criterion Cr1 says that if |e1*Y|>|e2*X| then
variation in X is more "exogenous or independent" than in Y,
and the causal path is X to Y. Criterion Cr2 requires
|e2|<|e1|. These inequalities between many absolute values are
quantified by four orders of stochastic dominance. Our third
criterion Cr3, for the causal path X to Y, requires new
generalized partial correlations to satisfy |r*(x|y,z)|<
|r*(y|x,z)|. The function parcorVec() reports generalized
partials between the first variable and all others. The
package provides several R functions including get0outliers()
for outlier detection, bigfp() for numerical integration by the
trapezoidal rule, stochdom2() for stochastic dominance,
pillar3D() for 3D charts, canonRho() for generalized canonical
correlations, depMeas() measures nonlinear dependence, and
causeSummary(mtx) reports summary of causal paths among matrix
columns. Portfolio selection: decileVote(), momentVote(),
dif4mtx(), exactSdMtx() can rank several stocks. Functions
whose names begin with 'boot' provide bootstrap statistical
inference, including a new bootGcRsq() test for
"Granger-causality" allowing nonlinear relations. A new tool
for evaluation of out-of-sample portfolio performance is
outOFsamp(). Panel data implementation is now included. See
eight vignettes of the package for theory, examples, and usage
tips. See Vinod (2019) \doi{10.1080/03610918.2015.1122048}.
