nonlintest function

Test of Non-linearity of a Time Series

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

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).

Returns

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).

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 c("$X_t=\\alpha\n$", "$X_{t-1}\\varepsilon_{t-1} +\\varepsilon_t$").

Examples

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

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

Author(s)

Adrian Barnett a.barnett@qut.edu.au