Teraesvirta Neural Network Test for Nonlinearity

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

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

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.

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.

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.

Author

A. Trapletti

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)
#> 
#> 	Teraesvirta Neural Network Test
#> 
#> data:  x and y
#> X-squared = 2539.9, df = 2, p-value < 2.2e-16
#> 

## Is the polynomial of order 2 misspecified?
terasvirta.test(cbind(x,x^2,x^3), y)
#> 
#> 	Teraesvirta Neural Network Test
#> 
#> data:  cbind(x, x^2, x^3) and y
#> X-squared = 3.8829, df = 16, p-value = 0.9991
#> 

## 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)
#> 
#> 	Teraesvirta Neural Network Test
#> 
#> data:  x
#> X-squared = 129.42, df = 2, p-value < 2.2e-16
#>