npRmpi (version 0.60-20)

npdeptest: Kernel Consistent Pairwise Nonlinear Dependence Test for Univariate Processes

Description

npdeptest implements the consistent metric entropy test of pairwise independence as described in Maasoumi and Racine (2002).

Usage

npdeptest(data.x = NULL,
          data.y = NULL,
          method = c("integration","summation"),
          bootstrap = TRUE,
          boot.num = 399,
          random.seed = 42)

Value

npdeptest returns an object of type deptest with the following components

Srho

the statistic Srho

Srho.bootstrap.vec

contains the bootstrap replications of Srho

P

the P-value of the Srho statistic

bootstrap

a logical value indicating whether bootstrapping was performed

boot.num

number of bootstrap replications

bw.data.x

the numeric bandwidth for data.x marginal density

bw.data.y

the numeric bandwidth for data.y marginal density

bw.joint

the numeric matrix of bandwidths for data and lagged data joint density at lag num.lag

summary supports object of type deptest.

Arguments

data.x, data.y

two univariate vectors containing two variables that are of type numeric.

method

a character string used to specify whether to compute the integral version or the summation version of the statistic. Can be set as integration or summation (see below for details). Defaults to integration.

bootstrap

a logical value which specifies whether to conduct the bootstrap test or not. If set to FALSE, only the statistic will be computed. Defaults to TRUE.

boot.num

an integer value specifying the number of bootstrap replications to use. Defaults to 399.

random.seed

an integer used to seed R's random number generator. This is to ensure replicability. Defaults to 42.

Author

Tristen Hayfield , Jeffrey S. Racine

Usage Issues

The integration version of the statistic uses multidimensional numerical methods from the cubature package. See adaptIntegrate for details. The integration version of the statistic will be substantially slower than the summation version, however, it will likely be both more accurate and powerful.

Details

npsdeptest computes the nonparametric metric entropy (normalized Hellinger of Granger, Maasoumi and Racine (2004)) for testing pairwise nonlinear dependence between the densities of two data series. See Maasoumi and Racine (2002) for details. Default bandwidths are of the Kullback-Leibler variety obtained via likelihood cross-validation. The null distribution is obtained via bootstrap resampling under the null of pairwise independence.

npdeptest computes the distance between the joint distribution and the product of marginals (i.e. the joint distribution under the null), \(D[f(y, \hat y), f(y)\times f(\hat y)]\). Examples include, (a) a measure/test of “fit”, for in-sample values of a variable \(y\) and its fitted values, \(\hat y\), and (b) a measure of “predictability” for a variable \(y\) and its predicted values \(\hat y\) (from a user implemented model).

The summation version of this statistic will be numerically unstable when data.x and data.y lack common support or are sparse (the summation version involves division of densities while the integration version involves differences). Warning messages are produced should this occur (‘integration recommended’) and should be heeded.

References

Granger, C.W. and E. Maasoumi and J.S. Racine (2004), “A dependence metric for possibly nonlinear processes”, Journal of Time Series Analysis, 25, 649-669.

Maasoumi, E. and J.S. Racine (2002), “Entropy and Predictability of Stock Market Returns,” Journal of Econometrics, 107, 2, pp 291-312.

See Also

npdeneqtest,npsdeptest,npsymtest,npunitest

Examples

if (FALSE) {
## Not run in checks: excluded to keep MPI examples stable and check times short.
## The following example is adapted for interactive parallel execution
## in R. Here we spawn 1 slave so that there will be two compute nodes
## (master and slave).  Kindly see the batch examples in the demos
## directory (npRmpi/demos) and study them carefully. Also kindly see
## the more extensive examples in the np package itself. See the npRmpi
## vignette for further details on running parallel np programs via
## vignette("npRmpi",package="npRmpi").

## Start npRmpi for interactive execution. If slaves are already running and
## `options(npRmpi.reuse.slaves=TRUE)` (default on some systems), this will
## reuse the existing pool instead of respawning. To change the number of
## slaves, call `npRmpi.stop(force=TRUE)` then restart.
npRmpi.start(nslaves=1)

mpi.bcast.cmd(set.seed(42),
              caller.execute=TRUE)

n <- 100

x <- rnorm(n)
y <- 1 + x + rnorm(n)
model <- lm(y~x)
y.fit <- fitted(model)
     
mpi.bcast.Robj2slave(y)
mpi.bcast.Robj2slave(y.fit)

mpi.bcast.cmd(output <- npdeptest(y,
                                  y.fit,
                                  boot.num=29,
                                  method="summation"),
              caller.execute=TRUE)

summary(output)

## For the interactive run only we close the slaves perhaps to proceed
## with other examples and so forth. This is redundant in batch mode.

## Note: on some systems (notably macOS+MPICH), repeatedly spawning and
## tearing down slaves in the same R session can lead to hangs/crashes.
## npRmpi may therefore keep slave daemons alive by default and
## `npRmpi.stop()` performs a "soft close". Use `force=TRUE` to
## actually shut down the slaves.
##
## You can disable reuse via `options(npRmpi.reuse.slaves=FALSE)` or by
## setting the environment variable `NP_RMPI_NO_REUSE_SLAVES=1` before
## loading the package.

npRmpi.stop()               ## soft close (may keep slaves alive)
## npRmpi.stop(force=TRUE)  ## hard close

## Note that in order to exit npRmpi properly avoid quit(), and instead
## use mpi.quit() as follows.

## mpi.bcast.cmd(mpi.quit(),
##               caller.execute=TRUE)
}