np (version 0.40-13)

npsdeptest: 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.

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 multdimensional 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 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.

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

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")