nonlintest: Test of non-linearity of a time series
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Description Usage Arguments Details Value Author(s) References See Also Examples

A bootstrap test of non-linearity in a time series using the third-order moment.

1	nonlintest(data, n.lag, n.boot, alpha=0.05)

`data`	a vector of equally spaced numeric observations (time series).
`n.lag`	the number of lags tested using the third-order moment, maximum = length of time series.
`n.boot`	the number of bootstrap replications (suggested minimum of 100; 1000 or more would be better).
`alpha`	statistical significance level of test (default=0.05).

The test uses aaft to create linear surrogates with the same second-order properties, but no (third-order) non-linearity. The third-order moments (third) of these linear surrogates and the actual series are then compared from lags 0 up to n.lag (excluding the skew at the co-ordinates (0,0)). The bootstrap test works on the overall area outside the limits, and gives an indication of the overall non-linearity. The plot using region shows those co-ordinates of the third order moment that exceed the null hypothesis limits, and can be a useful clue for guessing the type of non-linearity. For example, a large value at the co-ordinates (0,1) might be caused by a bi-linear series X_t=α X_{t-1}\varepsilon_{t-1} +\varepsilon_t.

Returns an object of class “nonlintest” with the following parts:

`region`	the region of the third order moment where the test exceeds the limits (up to `n.lag`).
`n.lag`	the maximum lag tested using the third-order moment.
`stats`	a list of following statistics for the area outside the test limits:
`outside`	the total area outside of limits (summed over the whole third-order moment).
`stan`	the total area outside the limits divided by its standard deviation to give a standardised estimate.
`median`	the median area outside the test limits.
`upper`	the (1-`alpha`)th percentile of the area outside the limits.
`pvalue`	Bootstrap p-value of the area outside the limits to test if the series is linear.
`test`	Reject the null hypothesis that the series is linear (TRUE/FALSE).