white.test {tseries}

White Neural Network Test for Nonlinearity

Description

Generically computes the White neural network test for neglected nonlinearity either for the time series x or the regression y~x.

Usage

## S3 method for class 'ts'
white.test(x, lag = 1, qstar = 2, q = 10, range = 4, 
            type = c("Chisq","F"), scale = TRUE, ...)
## Default S3 method:
white.test(x, y, qstar = 2, q = 10, range = 4,
            type = c("Chisq","F"), scale = TRUE, ...)

Arguments

x

a numeric vector, matrix, or time series.

y

a numeric vector.

lag

an integer which specifies the model order in terms of lags.

q

an integer representing the number of phantom hidden units used to compute the test statistic.

qstar

the test is conducted using qstar principal components of the phantom hidden units. The first principal component is omitted since in most cases it appears to be collinear with the input vector of lagged variables. This strategy preserves power while still conserving degrees of freedom.

range

the input to hidden unit weights are initialized uniformly over [-range/2, range/2].

type

a string indicating whether the Chi-Squared test or the F-test is computed. Valid types are "Chisq" and "F".

scale

a logical indicating whether the data should be scaled before computing the test statistic. The default arguments to scale are used.

...

further arguments to be passed from or to methods.

Details

The null is the hypotheses of linearity in “mean”. This type of test is consistent against arbitrary nonlinearity in mean. If type equals "F", then the F-statistic instead of the Chi-Squared statistic is used in analogy to the classical linear regression.

Missing values are not allowed.

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic.

p.value

the p-value of the test.

method

a character string indicating what type of test was performed.

parameter

a list containing the additional parameters used to compute the test statistic.

data.name

a character string giving the name of the data.

arguments

additional arguments used to compute the test statistic.

Author(s)

A. Trapletti

References

T. H. Lee, H. White, and C. W. J. Granger (1993): Testing for neglected nonlinearity in time series models. Journal of Econometrics 56, 269-290.

See Also

terasvirta.test

Examples

n <- 1000

x <- runif(1000, -1, 1)  # Non-linear in ``mean'' regression 
y <- x^2 - x^3 + 0.1*rnorm(x)
white.test(x, y)

## Is the polynomial of order 2 misspecified?
white.test(cbind(x,x^2,x^3), y)

## Generate time series which is nonlinear in ``mean''
x[1] <- 0.0
for(i in (2:n)) {
  x[i] <- 0.4*x[i-1] + tanh(x[i-1]) + rnorm(1, sd=0.5)
}
x <- as.ts(x)
plot(x)
white.test(x)