nonlintest: Test of Non-linearity of a Time Series

In season: Seasonal Analysis of Health Data

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).

Author(s)

Adrian Barnett [e-mail]

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

See Also

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.