# Generalized Correlations, Causal Paths and Portfolio Selection

## Documentation for package ‘generalCorr’ version 1.2.2

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

A B C D E G H I J K M N O P R S W

## -- A --

absBstdres | Block version of abs-stdres Absolute values of residuals of kernel regressions of standardized x on standardized y, no control variables.
absBstdresC | Block version of Absolute values of residuals of kernel regressions of standardized x on standardized y and control variables.
absBstdrhserC | Block version abs_stdrhser Absolute residuals kernel regressions of standardized x on y and control variables, Cr1 has abs(Resid*RHS).
abs_res | Absolute residuals of kernel regression of x on y.
abs_stdapd | Absolute values of gradients (apd's) of kernel regressions of x on y when both x and y are standardized.
abs_stdapdC | Absolute values of gradients (apd's) of kernel regressions of x on y when both x and y are standardized and control variables are present.
abs_stdres | Absolute values of residuals of kernel regressions of x on y when both x and y are standardized.
abs_stdresC | Absolute values of residuals of kernel regressions of x on y when both x and y are standardized and control variables are present (C for control presence).
abs_stdrhserC | Absolute residuals kernel regressions of standardized x on y and control variables, Cr1 has abs(RHS*y) not gradients.
abs_stdrhserr | Absolute values of Hausman-Wu null in kernel regressions of x on y when both x and y are standardized.
allPairs | Report causal identification for all pairs of variables in a matrix (deprecated function). It is better to choose a target variable and pair it with all others, instead of considering all possible targets.

## -- B --

badCol | internal badCol
bigfp | Compute the numerical integration by the trapezoidal rule.
bootDom12 | bootstrap confidence intervals for (x2-x1) exact SD1 to SD4 stochastic dominance .
bootGcLC | Compute vector of n999 nonlinear Granger causality paths
bootGcRsq | Compute vector of n999 nonlinear Granger causality paths
bootPair2 | Compute matrix of n999 rows and p-1 columns of bootstrap 'sum' (scores from Cr1 to Cr3).
bootPairs | Compute matrix of n999 rows and p-1 columns of bootstrap 'sum' (strength from Cr1 to Cr3).
bootPairs0 | Compute matrix of n999 rows and p-1 columns of bootstrap 'sum' index (strength from older criterion Cr1, with newer Cr2 and Cr3).
bootQuantile | Compute confidence intervals [quantile(s)] of indexes from bootPairs output
bootSign | Probability of unambiguously correct (+ or -) sign from bootPairs output
bootSignPcent | Probability of unambiguously correct (+ or -) sign from bootPairs output transformed to percentages.
bootSummary | Compute usual summary stats of 'sum' indexes from bootPairs output
bootSummary2 | Compute usual summary stats of 'sum' index in (-100, 100) from bootPair2

## -- C --

canonRho | Generalized canonical correlation, estimating alpha, beta, rho.
causeAllPair | All Pair Version Kernel (block) causality summary paths from three criteria
causeSum2Blk | Block Version 2: Kernel causality summary of causal paths from three criteria
causeSummary | Kernel causality summary of evidence for causal paths from three criteria
causeSummary0 | Older Kernel causality summary of evidence for causal paths from three criteria
causeSummary2 | Kernel causality summary of evidence for causal paths from three criteria using new exact stochastic dominance. The function develops a unanimity index regarding the which flip (y on xi) or (xi on y) is best. Relevant signs determine the causal direction and unanimity index among three criteria. While allowing the researcher to keep some variables as controls, or outside the scope of causal path determination (e.g., age or latitude) this function produces detailed causal path information in a 5 column matrix identifying the names of variables, causal path directions, path strengths re-scaled to be in the range [-100, 100], (table reports absolute values of the strength) plus Pearson correlation and its p-value. The '2' in the name of the function suggests a second implementation where exact stochastic dominance, decileVote and momentVote are used and where we avoid Anderson's trapezoidal approximation.
causeSummBlk | Block Version 2: Kernel causality summary of causal paths from three criteria
causeSumNoP | No print (NoP) version of causeSummBlk summary causal paths from three criteria
cofactor | Compute cofactor of a matrix based on row r and column c.
compPortfo | Compares two vectors (portfolios) using momentVote, DecileVote and exactSdMtx functions.
comp_portfo2 | Compares two vectors (portfolios) using stochastic dominance of orders 1 to 4.

## -- D --

da | internal da
da2Lag | internal da2Lag
decileVote | Function compares nine deciles of stock return distributions.
depMeas | depMeas Signed measure of nonlinear nonparametric dependence between two vectors.
dif4 | order 4 differencing of a time series vector
dif4mtx | order four differencing of a matrix of time series
diff.e0 | Internal diff.e0
dig | Internal dig

## -- E --

e0 | internal e0
EuroCrime | European Crime Data
exactSdMtx | Exact stochastic dominance computation from areas above ECDF pillars.

## -- G --

GcRsqX12 | Generalized Granger-Causality. If dif>0, x2 Granger-causes x1.
GcRsqX12c | Generalized Granger-Causality. If dif>0, x2 Granger-causes x1.
GcRsqYX | Nonlinear Granger causality between two time series workhorse function.
GcRsqYXc | Nonlinear Granger causality between two time series workhorse function.(local constant version)
generalCorrInfo | generalCorr package description:
get0outliers | Function to compute outliers and their count using Tukey method using 1.5 times interquartile range (IQR) to define boundaries.
getSeq | Two sequences: starting+ending values from n and blocksize (internal use)
gmc0 | internal gmc0
gmc1 | internal gmc1
gmcmtx0 | Matrix R* of generalized correlation coefficients captures nonlinearities.
gmcmtxBlk | Matrix R* of generalized correlation coefficients captures nonlinearities using blocks.
gmcmtxZ | compute the matrix R* of generalized correlation coefficients.
gmcxy_np | Function to compute generalized correlation coefficients r*(x|y) and r*(y|x) from two vectors (not matrices)
goodCol | internal goodCol

## -- H --

heurist | Heuristic t test of the difference between two generalized correlations.

## -- I --

i | internal i
ibad | internal object
ii | internal ii

## -- J --

j | internal j

## -- K --

kern | Kernel regression with options for residuals and gradients.
kern2 | Kernel regression version 2 with optional residuals and gradients with regtype="ll" for local linear, bwmethod="cv.aic" for AIC-based bandwidth selection.
kern2ctrl | Kernel regression with control variables and optional residuals and gradients. version 2 regtype="ll" for local linear, bwmethod="cv.aic" for AIC-based bandwidth selection. It admits control variables.
kern_ctrl | Kernel regression with control variables and optional residuals and gradients.

## -- M --

mag | Approximate overall magnitudes of kernel regression partials dx/dy and dy/dx.
mag_ctrl | After removing control variables, magnitude of effect of x on y, and of y on x.
min.e0 | internal min.e0
minor | Function to do compute the minor of a matrix defined by row r and column c.
momentVote | Function compares Pearson Stats and Sharpe Ratio for a matrix of stock returns
mtx | internal mtx
mtx0 | internal mtx0
mtx2 | internal mtx2

## -- N --

n | internal n
nall | internal nall
nam.badCol | internal nam.badCol
nam.goodCol | internal nam.goodCol
nam.mtx0 | internal nam.mtx0
napair | Function to do pairwise deletion of missing rows.
naTriple | Function to do matched deletion of missing rows from x, y and z variable(s).
naTriplet | Function to do matched deletion of missing rows from x, y and control variable(s).
NLhat | Compute fitted values from kernel regression of x on y and y on x

## -- O --

out1 | internal out1
outOFsamp | Compare out-of-sample portfolio choice algorithms by a leave-percent-out method.

## -- P --

p1 | internal p1
Panel2Lag | Function to compute a vector of 2 lagged values of a variable from panel data.
PanelLag | Function for computing a vector of one-lagged values of xj, a variable from panel data.
parcorBijk | Block version of generalized partial correlation coefficients between Xi and Xj, after removing the effect of xk, via nonparametric regression residuals.
parcorBMany | Block version reports many generalized partial correlation coefficients allowing control variables.
parcorHijk | Generalized partial correlation coefficients between Xi and Xj, after removing the effect of Xk, via OLS regression residuals.
parcorHijk2 | Generalized partial correlation coefficients between Xi and Xj,
parcorMany | Report many generalized partial correlation coefficients allowing control variables.
parcorMtx | Matrix of generalized partial correlation coefficients, always leaving out control variables, if any.
parcorSilent | Silently compute generalized (ridge-adjusted) partial correlation coefficients from matrix R*.
parcorVec | Vector of generalized partial correlation coefficients (GPCC), always leaving out control variables, if any.
parcorVecH | Vector of hybrid generalized partial correlation coefficients.
parcorVecH2 | Vector of hybrid generalized partial correlation coefficients.
parcor_ijk | Generalized partial correlation coefficients between Xi and Xj, after removing the effect of xk, via nonparametric regression residuals.
parcor_ijkOLD | Generalized partial correlation coefficient between Xi and Xj after removing the effect of all others. (older version, deprecated)
parcor_linear | Partial correlation coefficient between Xi and Xj after removing the linear effect of all others.
parcor_ridg | Compute generalized (ridge-adjusted) partial correlation coefficients from matrix R*. (deprecated)
pcause | Compute the bootstrap probability of correct causal direction.
pillar3D | Create a 3D pillar chart to display (x, y, z) data coordinate surface.
prelec2 | Intermediate weighting function giving Non-Expected Utility theory weights.
probSign | Compute probability of positive or negative sign from bootPairs output

## -- R --

rank2return | Compute the portfolio return knowing the rank of a stock in the input 'mtx'.
rhs.lag2 | internal rhs.lag2
rhs1 | internal rhs1
ridgek | internal ridgek
rij | internal rij
rijMrji | internal rijMrji
rji | internal rji
rrij | internal rrij
rrji | internal rrji
rstar | Function to compute generalized correlation coefficients r*(x,y).

## -- S --

sales2Lag | internal sales2Lag
salesLag | internal salesLag
seed | internal seed
sgn.e0 | internal sgn.e0
silentMtx | No-print kernel-causality unanimity score matrix with optional control variables
silentMtx0 | Older kernel-causality unanimity score matrix with optional control variables
silentPair2 | kernel causality (version 2) scores with control variables
silentPairs | No-print kernel causality scores with control variables Hausman-Wu Criterion 1
silentPairs0 | Older version, kernel causality weighted sum allowing control variables
siPair2Blk | Block Version of silentPair2 for causality scores with control variables
siPairsBlk | Block Version of silentPairs for causality scores with control variables
some0Pairs | Function reporting detailed kernel causality results in a 7-column matrix (uses deprecated criterion 1, no longer recommended but may be useful for second and third criterion typ=2,3)
someCPairs | Kernel causality computations admitting control variables.
someCPairs2 | Kernel causality computations admitting control variables reporting a 7-column matrix, version 2.
someMagPairs | Summary magnitudes after removing control variables in several pairs where dependent variable is fixed.
somePairs | Function reporting kernel causality results as a 7-column matrix.(deprecated)
somePairs2 | Function reporting kernel causality results as a 7-column matrix, version 2.
sort.abse0 | internal sort.abse0
sort.e0 | internal sort.e0
sort_matrix | Sort all columns of matrix x with respect to the j-th column.
stdres | Residuals of kernel regressions of x on y when both x and y are standardized.
stdz_xy | Standardize x and y vectors to achieve zero mean and unit variance.
stochdom2 | Compute vectors measuring stochastic dominance of four orders.
sudoCoefParcor | Pseudo regression coefficients from generalized partial correlation coefficients, (GPCC).
sudoCoefParcorH | Peudo regression coefficients from hybrid generalized partial correlation coefficients (HGPCC).
summaryRank | Compute ranks of rows of matrix and summarize them into a choice suggestion.
symmze | Replace asymmetric matrix by max of abs values of [i,j] or [j,i] elements.

## -- W --

wtdpapb | Creates input for the stochastic dominance function stochdom2