np.sdeptest: Kernel Consistent Serial Dependence Test for Univariate...

In np: Nonparametric Kernel Smoothing Methods for Mixed Data Types

Kernel Consistent Serial Dependence Test for Univariate Nonlinear Processes

Description

npsdeptest implements the consistent metric entropy test of nonlinear serial dependence as described in Granger, Maasoumi and Racine (2004).

Usage

npsdeptest(data = NULL,
           lag.num = 1,
           method = c("integration","summation"),
           bootstrap = TRUE,
           boot.num = 399,
           random.seed = 42)

Arguments

data	a vector containing the variable that can be of type numeric or ts.
lag.num	an integer value specifying the maximum number of lags to use. Defaults to 1.
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 for nonlinear serial dependence, D[f(y_t, \hat y_{t-k}), f(y_t)\times f(\hat y_{t-k})]. Default bandwidths are of the Kullback-Leibler variety obtained via likelihood cross-validation.

The test may be applied to a raw data series or to residuals of user estimated models.

The summation version of this statistic may be numerically unstable when data is 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

npsdeptest returns an object of type deptest with the following components

Srho	the statistic vector Srho
Srho.cumulant	the cumulant statistic vector Srho.cumulant
Srho.bootstrap.mat	contains the bootstrap replications of Srho
Srho.cumulant.bootstrap.mat	contains the bootstrap replications of Srho.cumulant
P	the P-value vector of the Srho statistic vector
P.cumulant	the P-value vector of the cumulant Srho statistic vector
bootstrap	a logical value indicating whether bootstrapping was performed
boot.num	number of bootstrap replications
lag.num	the number of lags
bw.y	the numeric vector of bandwidths for data marginal density at lag num.lag
bw.y.lag	the numeric vector of bandwidths for lagged data marginal density at lag num.lag
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 [e-mail], Jeffrey S. Racine [e-mail]

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.

See Also

npdeptest,npdeneqtest,npsymtest,npunitest

Examples

## Not run: 
set.seed(1234)

## A function to create a time series

ar.series <- function(phi,epsilon) {
  n <- length(epsilon)
  series <- numeric(n)
  series[1] <- epsilon[1]/(1-phi)
  for(i in 2:n) {
    series[i] <- phi*series[i-1] + epsilon[i]
  }
  return(series)
}

n <- 100

## Stationary persistent time-series

yt <- ar.series(0.95,rnorm(n))
npsdeptest(yt,lag.num=2,boot.num=99,method="summation")

Sys.sleep(5)

## Stationary independent time-series

yt <- ar.series(0.0,rnorm(n))
npsdeptest(yt,lag.num=2,boot.num=99,method="summation")

## Stationary persistent time-series

yt <- ar.series(0.95,rnorm(n))
npsdeptest(yt,lag.num=2,boot.num=99,method="integration")

Sys.sleep(5)

## Stationary independent time-series

yt <- ar.series(0.0,rnorm(n))
npsdeptest(yt,lag.num=2,boot.num=99,method="integration")


## End(Not run) 

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