# nonlintest: Test of Non-linearity of a Time Series In season: Seasonal Analysis of Health Data

 nonlintest R Documentation

## Test of Non-linearity of a Time Series

### Description

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

### Usage

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

### Arguments

 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).

### Details

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.

### Value

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).

### References

Barnett AG & Wolff RC (2005) A Time-Domain Test for Some Types of Nonlinearity, IEEE Transactions on Signal Processing, vol 53, pages 26–33

print.nonlintest, plot.nonlintest

### Examples

data(CVD)
## Not run: test.res = nonlintest(data=CVD\$cvd, n.lag=4, n.boot=1000)

season documentation built on March 21, 2022, 9:10 a.m.