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, y-hat),
f(y)*f(y-hat)]. Examples include, (a) a measure/test of “fit”,
for in-sample values of a variable y and its fitted values,
y-hat, and (b) a measure of “predictability” for
a variable y and its predicted values y-hat (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.
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
## 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)