# terasvirta.test

From tseries v0.8-3
by Kurt Hornik

##### 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`

.

- Keywords
- ts

##### 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.

##### 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.

##### See Also

##### 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)
```

*Documentation reproduced from package tseries, version 0.8-3, License: GPL (see file COPYING), except for ./src/muin2ser.f and ./misc which are free for non-commercial purposes. See file README for details.*

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