# np.deptest: Kernel Consistent Pairwise Nonlinear Dependence Test for... In np: Nonparametric Kernel Smoothing Methods for Mixed Data Types

 npdeptest R Documentation

## 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)



### 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.

### 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.

### 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.

### 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.

### Author(s)

Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca

### 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.

npdeneqtest,npsdeptest,npsymtest,npunitest

### Examples

## Not run:
set.seed(1234)

## Test/measure lack of fit between y and its fitted value from a
## regression model when x is relevant using the summation' version.

n <- 100
x <- rnorm(n)
y <- 1 + x + rnorm(n)
model <- lm(y~x)
y.fit <- fitted(model)

npdeptest(y,y.fit,boot.num=99,method="summation")

Sys.sleep(5)

## Test/measure lack of fit between y and its fitted value from a
## regression model when x is irrelevant using the summation' version.

n <- 100
x <- runif(n,-2,2)
y <- 1 + rnorm(n)
model <- lm(y~x)
y.fit <- fitted(model)

npdeptest(y,y.fit,boot.num=99,method="summation")

## Test/measure lack of fit between y and its fitted value from a
## regression model when x is relevant using the integration'
## version (default, slower than summation version).

n <- 100
x <- rnorm(n)
y <- 1 + x + rnorm(n)
model <- lm(y~x)
y.fit <- fitted(model)

npdeptest(y,y.fit,boot.num=99)

Sys.sleep(5)

## Test/measure lack of fit between y and its fitted value from a
## regression model when x is irrelevant using the integration'
## version (default, slower than summation version).

n <- 100
x <- runif(n,-2,2)
y <- 1 + rnorm(n)
model <- lm(y~x)
y.fit <- fitted(model)

npdeptest(y,y.fit,boot.num=99)

## End(Not run)


np documentation built on March 31, 2023, 9:41 p.m.