tseries (version 0.10-24)

terasvirta.test: Teraesvirta Neural Network Test for Nonlinearity

Description

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

Usage

## S3 method for class 'ts':
terasvirta.test(x, lag = 1, type = c("Chisq","F"),
                scale = TRUE, ...)
## S3 method for class 'default':
terasvirta.test(x, y, 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.

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.

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.

Details

The null is the hypotheses of linearity in ``mean''. This test uses a Taylor series expansion of the activation function to arrive at a suitable test statistic. 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.

References

T. Teraesvirta, C. F. Lin, and C. W. J. Granger (1993): Power of the Neural Network Linearity Test. Journal of Time Series Analysis 14, 209-220.

See Also

white.test

Examples

n <- 1000

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

## Is the polynomial of order 2 misspecified?
terasvirta.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)
terasvirta.test(x)