nonlintest | R Documentation |
A bootstrap test of non-linearity in a time series using the third-order moment.
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 |
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- |
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). |
Adrian Barnett a.barnett@qut.edu.au
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
data(CVD) ## Not run: test.res = nonlintest(data=CVD$cvd, n.lag=4, n.boot=1000)
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