third function

Third-order Moment

Estimated third order moment for a time series.

third(data, n.lag, centre = TRUE, outmax = TRUE, plot = TRUE)

Arguments

• data: a vector of equally spaced numeric observations (time series).
• n.lag: the number of lags, maximum = length of time series.
• centre: centre series by subtracting mean (default=TRUE).
• outmax: display the (x,y) lag co-ordinates for the maximum and minimum values (default=TRUE).
• plot: contour plot of the third order moment (default=TRUE).

Returns

• waxis: The axis --n.lag to n.lag.

• third: The estimated third order moment in the range --n.lag to n.lag, including the symmetries.

Details

The third-order moment is the extension of the second-order moment (essentially the autocovariance). The equation for the third order moment at lags (j,k) is: $n^{-1}\sum X_t X_{t+j} X_{t+k}$. The third-order moment is useful for testing for non-linearity in a time series, and is used by nonlintest.

Examples

data(CVD)
third(CVD$cvd, n.lag=12)

Author(s)

Adrian Barnett a.barnett@qut.edu.au